bzh666/mathvista_geo · Datasets at Hugging Face

problem stringlengths 281 746	answer stringlengths 1 21	proID stringlengths 1 3
<image>The Caption of this geometric diagram is:The internal angle bisectors OB and OC of triangle ABC intersect at point O. If ∠A = 110°, then ∠BOC = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	145°	3
<image>The Caption of this geometric diagram is:Find the measure of \angle HPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	97	5
<image>The Caption of this geometric diagram is:As shown in the figure, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6cm	6
<image>The Caption of this geometric diagram is:The figure shows a beautiful Pythagorean tree, where all quadrilaterals are squares and all triangles are right triangles. If the areas of squares A and B are 5 and 3 respectively, then the area of the largest square C is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	8	9
<image>The Caption of this geometric diagram is:As shown in the figure, in the right triangle ABC, ∠ACB = 90°, D is the midpoint of AB, and AB = 10. Then the length of CD is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	5	17
<image>The Caption of this geometric diagram is:$AB$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	8.5	28
<image>The Caption of this geometric diagram is:As shown in the figure, the two chords AB and CD in the circle intersect at E, ∠D = 35.0, ∠AEC = 105.0, then ∠C = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	70°	30
<image>The Caption of this geometric diagram is:As shown in the figure, in quadrilateral ABCD, AB = AC, ∠CAB = 40°, then the measure of ∠D is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	70°	32
<image>The Caption of this geometric diagram is:Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	4πcm	33
<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, EF and EB are chords of ⊙O, point E is the midpoint of arc FEB, EF intersects AB at point C, and OF is connected. If ∠AOF = 40°, then the degree measure of ∠F is (). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	35°	35
<image>The Caption of this geometric diagram is:Find the measure of \angle 3.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	38	48
<image>The Caption of this geometric diagram is:In the figure above, the ratio of the length of line AB to the length of line AC is 2 : 5. If AC = 25, what is the length of line AB?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	10	54
<image>The Caption of this geometric diagram is:As shown in the figure, a right triangle with a 60° angle has its vertex A and the right angle vertex C located on two parallel lines FG and DE, respectively. The hypotenuse AB bisects ∠CAG and intersects line DE at point H. What is the measure of ∠BCH?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	30°	55
<image>The Caption of this geometric diagram is:What is the perimeter of the rectangle?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	56
<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, CD is the chord of ⊙O, ∠ADC = 26.0, then the degree of ∠CAB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	64°	59
<image>The Caption of this geometric diagram is:As shown in the figure, points E and F are the midpoints of sides AB and AD of the rhombus ABCD, respectively, with AB = 5 and AC = 6. The length of EF is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	4	62
<image>The Caption of this geometric diagram is:What is the perimeter of the square?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	16	67
<image>The Caption of this geometric diagram is:A 16 cm elastic band AB is naturally stretched straight and fixed at both ends on a horizontal table. Then its midpoint C is pulled vertically upward by 6 cm to point D (as shown in the figure). How much longer is the elastic band stretched?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	4cm	68
<image>The Caption of this geometric diagram is:What is the perimeter of the rectangle?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	18	71
<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, C, and D are on circle O, and point E is on the extended line of AD. If ∠ABC = 60.0, then the degree of ∠CDE is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	60°	79
<image>The Caption of this geometric diagram is:A square is inscribed in a circle of area 18$\pi$ square units. Find the length of a side of the square.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	82
<image>The Caption of this geometric diagram is:A square is tangent to a line at point P in the figure above. What is the value of x?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	30	88
<image>The Caption of this geometric diagram is:As shown in the figure, point D is inside triangle ABC. CD bisects ∠ACB, BD⊥CD, ∠A＝∠ABD. If ∠DBC＝54°, then the degree measure of ∠A is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	27°	94
<image>The Caption of this geometric diagram is:As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	80°	95
<image>The Caption of this geometric diagram is:In the figure, KL is tangent to circle M at K. Find the value of x.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	9.45	114
<image>The Caption of this geometric diagram is:As shown in the figure, P is a point outside ⊙O, PA and PB intersect ⊙O at two points C and D respectively. It is known that the central angles of ⁀AB and ⁀CD are 90.0 and 50.0 respectively, then ∠P = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	20°	119
<image>The Caption of this geometric diagram is:As shown in the figure, in a 4×4 square grid where each small square has a side length of 1, points A, B, and C are all grid points. AD is perpendicular to BC at point D. Find the length of AD.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2	132
<image>The Caption of this geometric diagram is:As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	4.40米	141
<image>The Caption of this geometric diagram is:As shown in the figure, in the parallelogram ABCD, CE bisects ∠BCD and it intersects the AD edge at point E, and DE = 3.0, then the length of AB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	3	143
<image>The Caption of this geometric diagram is:As shown in the figure, line l1 ∥ l2, ∠1 = 50°, ∠2 = 75°, then ∠3 = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	55°	149
<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, and C are three points on ⊙O, and the straight line CD and ⊙O are tangent to point C. If ∠DCB = 40.0, then the degree of ∠CAB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	150
<image>The Caption of this geometric diagram is:As shown in the figure, lines l1 ∥ l2. A right triangle containing a 30° angle is placed as shown, with the right angle vertex on l2. If ∠1 = 76°, then ∠2 = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	44°	152
<image>The Caption of this geometric diagram is:Find the value of x.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	12	160
<image>The Caption of this geometric diagram is:As shown in the figure, in ▱ABCD, CE ⊥ AB, point E is the foot of perpendicular, if ∠D = 55.0, then ∠BCE = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	35°	164
<image>The Caption of this geometric diagram is:Find the length of $RS$ if $\triangle QRS$ is an equilateral triangle.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2	176
<image>The Caption of this geometric diagram is:As shown in the figure, points A and C are on the sides BF and BD of ∠FBD, respectively. BE bisects ∠FBD, and CE bisects ∠ACD. AE is connected. If ∠BEC = 35°, then the measure of ∠FAE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	55°	178
<image>The Caption of this geometric diagram is:As shown in the figure, in ABCD, given that AC = 4cm, if the perimeter of △ACD is 14cm, then the perimeter of ABCD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	20cm	179
<image>The Caption of this geometric diagram is:As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is α, AC ⊥ CD, BD ⊥ CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac{20}{3}	186
<image>The Caption of this geometric diagram is:As shown in the figure, the diameter CD of ⊙O crosses the midpoint G of chord EF, ∠DCF = 20.0, then ∠EOD is equal to ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	192
<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, points C and D are on ⊙O, ∠BCD = 25°, then the degree measure of ∠AOD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	130°	195
<image>The Caption of this geometric diagram is:As shown in the figure, in △ABC, points D, E, and F are the midpoints of sides BC, AD, and CE respectively, and S△ABC = 4 cm². Then S△DEF equals ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	0.5cm2	196
<image>The Caption of this geometric diagram is:As shown in the figure, in a 5×4 square grid, the side length of each small square is 1, and the vertices of triangle ABC are all at the vertices of these small squares. The value of tan∠BAC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac{4}{3}	203
<image>The Caption of this geometric diagram is:Find the scale factor from point Q to point Q'.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	3	206
<image>The Caption of this geometric diagram is:As shown in the figure, ⊙O is the circumscribed circle of the quadrilateral ABCD, if ∠O = 110.0, then the degree of ∠C is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	125°	220
<image>The Caption of this geometric diagram is:As shown in the figure, A, B, C are three points on ⊙O, ∠ACB = 25.0, then the degree of ∠BAO is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	65°	221
<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of circle O, DB and DC are respectively tangent to circle O at points B and C. If ∠ACE = 25.0, then the degree of ∠D is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	50°	228
<image>The Caption of this geometric diagram is:In the figure shown above, AC = 6. What is the length of segment AB?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	234
<image>The Caption of this geometric diagram is:Find the value of $z$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	12	236
<image>The Caption of this geometric diagram is:Find the length of line segment PTPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac { 20 } { 3 }	238
<image>The Caption of this geometric diagram is:Find the measure of \angle A of quadrilateral ABCDPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	135	242
<image>The Caption of this geometric diagram is:The area $A$ of the shaded region is given. Find the value of $x$. $A = 66$ cm$^2$ .Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	13.0	250
<image>The Caption of this geometric diagram is:As shown in the figure, ∠BAC = 110.0, if A and B are symmetrical with respect to the line MP, A and C are symmetrical with respect to the line NQ, then the size of ∠PAQ is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	255
<image>The Caption of this geometric diagram is:As shown in the figure, in triangle ABC, AD bisects ∠BAC and intersects BC at point D. DE⊥AB with the foot at E. If DE = 3 and AC = 4, then the area of triangle ADC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	256
<image>The Caption of this geometric diagram is:Construct squares outwardly on the three sides of a right triangle. The areas of two of the squares are shown in the figure. Find the area of square A ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	257
<image>The Caption of this geometric diagram is:As shown in the figure, the elevation angle of the top of a building is 30.0 when viewed from point A in the air by a hot air balloon, and the depression angle of this building is 60.0. The horizontal distance between the hot air balloon and the building is 120.0. The height of this building is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	160√{3}m	269
<image>The Caption of this geometric diagram is:As shown in the figure, points A and B are three points on ⊙O and AB = AC. Connect BO and CO, if ∠ABC = 65.0, then the degree of ∠BOC is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	100°	270
<image>The Caption of this geometric diagram is:Find the value of yPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	5	271
<image>The Caption of this geometric diagram is:One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	26	273
<image>The Caption of this geometric diagram is:As shown in the figure, AB, BC, CD, and DA are all tangents to the circle O. Given that AD = 2 and BC = 5, the value of AB + CD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	7	274
<image>The Caption of this geometric diagram is:As shown in the figure, in Rt△ABC, ∠BAC = 90.0, AD ⊥ BC at D, DE ⊥ AB at E, AD = 3.0, DE = 2.0, then the length of CD is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac{3√{5}}{2}	275
<image>The Caption of this geometric diagram is:As shown in the figure, it is known that the radius of ⊙O is 5.0 and the chord AB = 8.0, then the distance from the center O to AB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	3mm	276
<image>The Caption of this geometric diagram is:In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	60	280
<image>The Caption of this geometric diagram is:$arc XWY \cong arc XYT$. Find the value of $x$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	5	283
<image>The Caption of this geometric diagram is:As shown in the figure, it is known that AB is the diameter of ⊙O, if the degree of ∠BOC is 50.0, then the degree of ∠A is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	25°	285
<image>The Caption of this geometric diagram is:As shown in the figure, an elastic rubber band AB with a length of 8 cm is fixed at both ends on a horizontal table. Then, the midpoint C of the rubber band is pulled vertically upward by 3 cm to point D. At this point, the elastic rubber band is stretched by ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2cm	286
<image>The Caption of this geometric diagram is:As shown in the figure, parallel lines AB and CD are intersected by line AE. If ∠1 = 105°, then the degree measure of ∠2 is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	75°	290
<image>The Caption of this geometric diagram is:${HK}$ and ${IG}$ are diameters of $\odot L$. Find the $measure of arc {LIJ}$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	270	300
<image>The Caption of this geometric diagram is:The Caption of this geometric diagram is:${HK}$ and ${IG}$ are diameters of $\odot L$. Find the $measure of arc {LIJ}$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	100	304
<image>The Caption of this geometric diagram is:Find the value of zPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac { 40 } { 3 }	310
<image>The Caption of this geometric diagram is:In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	125*a^2 + 250	315
<image>The Caption of this geometric diagram is:As shown in the figure, given that points A, B, and C are on ⊙O, ∠AOB = 100.0, then the degree of ∠ACB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	50°	316
<image>The Caption of this geometric diagram is:Find the area of the figure. Round to the nearest tenth if necessary.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2256	318
<image>The Caption of this geometric diagram is:As shown in the figure, in triangle ABC, ∠C = 90°, AB = 13, AC = 5. D and E are the midpoints of AC and AB respectively. The length of DE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	320
<image>The Caption of this geometric diagram is:As shown in the figure, points A and B are separated by a pond. A point C is chosen outside AB such that point C can directly reach points A and B. Connect AC and BC, and find the midpoints M and N of AC and BC, respectively. If the measured length of MN is 20 m, then the distance between points A and B is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40m	322
<image>The Caption of this geometric diagram is:Find the value of tan(X)Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	\frac { 5 } { 12 }	333
<image>The Caption of this geometric diagram is:In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	8	338
<image>The Caption of this geometric diagram is:As shown in the figure, in ⊙O, AB = AC, ∠BAC = 70°, then the degree measure of ∠AEC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	55°	339
<image>The Caption of this geometric diagram is:In the figure above, which of the following is the greatest?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	d	342
<image>The Caption of this geometric diagram is:As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If ∠1 = 50.0, then the degree of ∠2 is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	130°	355
<image>The Caption of this geometric diagram is:If $\frac{IJ}{XJ}=\frac{HJ}{YJ}, measure of \angle WXJ=130$ and $measure \angle WZG=20,$ find the measure of \angle YIZPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	50	360
<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, and points C and D are on ⊙O. If ∠ABD = 50.0, then the degree of ∠BCD is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	364
<image>The Caption of this geometric diagram is:As shown in the figure, in the right triangle ABC, ∠ABC = 90°, points D, E, and F are the midpoints of sides AB, BC, and CA respectively. If DE + BF = 8, then the value of BF is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	4	371
<image>The Caption of this geometric diagram is:As shown in the figure, in the quadrilateral ABCD, ∠BAD = 120.0, ∠B = ∠D = 90.0, if you find a point M on BC and CD respectively, so that the perimeter of △AMN is the smallest, then the degree of ∠AMN + ∠ANM is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	120°	373
<image>The Caption of this geometric diagram is:Find the length of $AC$ in the isosceles triangle ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	7	375
<image>The Caption of this geometric diagram is:As shown in the figure, AD is the midline of triangle ABC, E is the midpoint of AD, and the area of triangle ABE is 2. Then the area of triangle ABC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	8	378
<image>The Caption of this geometric diagram is:Find the value of xPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	10 \sqrt { 3 }	386
<image>The Caption of this geometric diagram is:Express the ratio of $\tan M$ as a decimal to the nearest hundredth.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	0.42	388
<image>The Caption of this geometric diagram is:As shown in the figure, point O is the center of ⊙O, points A, B, and C are on ⊙O, AO ∥ BC, ∠AOB = 40.0, then the degree of ∠OAC is equal to ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	20°	391
<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, and C are all on ⊙O with a radius of 2, and ∠C＝30°. Find the length of chord AB.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2	397
<image>The Caption of this geometric diagram is:What is the perimeter of the shape?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6	399
<image>The Caption of this geometric diagram is:Find the length of TX if $E X=24$ and $D E=7$Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	32	403
<image>The Caption of this geometric diagram is:As shown in the figure, points B, D, E, and C lie on the same straight line. If △ABD ≌ △ACE and ∠AEC = 110°, then the measure of ∠DAE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	407
<image>The Caption of this geometric diagram is:Find the value of z.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	6 \sqrt { 5 }	408
<image>The Caption of this geometric diagram is:Find the perimeter of $\triangle DEF,$ if $\triangle DEF \sim \triangle CBF,$ perimeter of $\triangle CBF=27, DF=6,$ and $FC=8$Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	20.25	410
<image>The Caption of this geometric diagram is:Given: As shown in the figure, in triangle ABC, AB = AC, BD is the bisector of ∠ABC, and ∠BDC = 75°. Find the degree measure of ∠A.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	40°	413
<image>The Caption of this geometric diagram is:If $ST=8, TR=4$, and $PT=6$, find the length of $QR$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	9	414
<image>The Caption of this geometric diagram is:In a right triangle ABC, ∠C = 90°, if AC = 6 and BC = 8, then the value of cos A is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	0.6	425
<image>The Caption of this geometric diagram is:As shown in the figure, if DE is the midline of △ABC and the perimeter of △ADE is 1, then the perimeter of △ABC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	2	426
<image>The Caption of this geometric diagram is:In the figure above, side AC of triangle ABC is on line l. What is x in terms of k?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	60-k	434
<image>The Caption of this geometric diagram is:What is the perimeter of the shape?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.	9	441

<image>The Caption of this geometric diagram is:The internal angle bisectors OB and OC of triangle ABC intersect at point O. If ∠A = 110°, then ∠BOC = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

145°

3

<image>The Caption of this geometric diagram is:Find the measure of \angle HPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

97

5

<image>The Caption of this geometric diagram is:As shown in the figure, if CB = 4.0, DB = 7.0, and D is the midpoint of AC, then the length of AC is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6cm

6

<image>The Caption of this geometric diagram is:The figure shows a beautiful Pythagorean tree, where all quadrilaterals are squares and all triangles are right triangles. If the areas of squares A and B are 5 and 3 respectively, then the area of the largest square C is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

8

9

<image>The Caption of this geometric diagram is:As shown in the figure, in the right triangle ABC, ∠ACB = 90°, D is the midpoint of AB, and AB = 10. Then the length of CD is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

5

17

<image>The Caption of this geometric diagram is:$AB$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the radius of the circle.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

8.5

28

<image>The Caption of this geometric diagram is:As shown in the figure, the two chords AB and CD in the circle intersect at E, ∠D = 35.0, ∠AEC = 105.0, then ∠C = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

70°

30

<image>The Caption of this geometric diagram is:As shown in the figure, in quadrilateral ABCD, AB = AC, ∠CAB = 40°, then the measure of ∠D is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

70°

32

<image>The Caption of this geometric diagram is:Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

4πcm

33

<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, EF and EB are chords of ⊙O, point E is the midpoint of arc FEB, EF intersects AB at point C, and OF is connected. If ∠AOF = 40°, then the degree measure of ∠F is (). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

35°

35

<image>The Caption of this geometric diagram is:Find the measure of \angle 3.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

38

48

<image>The Caption of this geometric diagram is:In the figure above, the ratio of the length of line AB to the length of line AC is 2 : 5. If AC = 25, what is the length of line AB?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

10

54

<image>The Caption of this geometric diagram is:As shown in the figure, a right triangle with a 60° angle has its vertex A and the right angle vertex C located on two parallel lines FG and DE, respectively. The hypotenuse AB bisects ∠CAG and intersects line DE at point H. What is the measure of ∠BCH?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

30°

55

<image>The Caption of this geometric diagram is:What is the perimeter of the rectangle?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

56

<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, CD is the chord of ⊙O, ∠ADC = 26.0, then the degree of ∠CAB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

64°

59

<image>The Caption of this geometric diagram is:As shown in the figure, points E and F are the midpoints of sides AB and AD of the rhombus ABCD, respectively, with AB = 5 and AC = 6. The length of EF is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

4

62

<image>The Caption of this geometric diagram is:What is the perimeter of the square?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

16

67

<image>The Caption of this geometric diagram is:A 16 cm elastic band AB is naturally stretched straight and fixed at both ends on a horizontal table. Then its midpoint C is pulled vertically upward by 6 cm to point D (as shown in the figure). How much longer is the elastic band stretched?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

4cm

68

<image>The Caption of this geometric diagram is:What is the perimeter of the rectangle?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

18

71

<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, C, and D are on circle O, and point E is on the extended line of AD. If ∠ABC = 60.0, then the degree of ∠CDE is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

60°

79

<image>The Caption of this geometric diagram is:A square is inscribed in a circle of area 18$\pi$ square units. Find the length of a side of the square.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

82

<image>The Caption of this geometric diagram is:A square is tangent to a line at point P in the figure above. What is the value of x?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

30

88

<image>The Caption of this geometric diagram is:As shown in the figure, point D is inside triangle ABC. CD bisects ∠ACB, BD⊥CD, ∠A＝∠ABD. If ∠DBC＝54°, then the degree measure of ∠A is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

27°

94

<image>The Caption of this geometric diagram is:As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

80°

95

<image>The Caption of this geometric diagram is:In the figure, KL is tangent to circle M at K. Find the value of x.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

9.45

114

<image>The Caption of this geometric diagram is:As shown in the figure, P is a point outside ⊙O, PA and PB intersect ⊙O at two points C and D respectively. It is known that the central angles of ⁀AB and ⁀CD are 90.0 and 50.0 respectively, then ∠P = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

20°

119

<image>The Caption of this geometric diagram is:As shown in the figure, in a 4×4 square grid where each small square has a side length of 1, points A, B, and C are all grid points. AD is perpendicular to BC at point D. Find the length of AD.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2

132

<image>The Caption of this geometric diagram is:As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

4.40米

141

<image>The Caption of this geometric diagram is:As shown in the figure, in the parallelogram ABCD, CE bisects ∠BCD and it intersects the AD edge at point E, and DE = 3.0, then the length of AB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

3

143

<image>The Caption of this geometric diagram is:As shown in the figure, line l1 ∥ l2, ∠1 = 50°, ∠2 = 75°, then ∠3 = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

55°

149

<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, and C are three points on ⊙O, and the straight line CD and ⊙O are tangent to point C. If ∠DCB = 40.0, then the degree of ∠CAB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

150

<image>The Caption of this geometric diagram is:As shown in the figure, lines l1 ∥ l2. A right triangle containing a 30° angle is placed as shown, with the right angle vertex on l2. If ∠1 = 76°, then ∠2 = ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

44°

152

<image>The Caption of this geometric diagram is:Find the value of x.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

12

160

<image>The Caption of this geometric diagram is:As shown in the figure, in ▱ABCD, CE ⊥ AB, point E is the foot of perpendicular, if ∠D = 55.0, then ∠BCE = ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

35°

164

<image>The Caption of this geometric diagram is:Find the length of $RS$ if $\triangle QRS$ is an equilateral triangle.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2

176

<image>The Caption of this geometric diagram is:As shown in the figure, points A and C are on the sides BF and BD of ∠FBD, respectively. BE bisects ∠FBD, and CE bisects ∠ACD. AE is connected. If ∠BEC = 35°, then the measure of ∠FAE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

55°

178

<image>The Caption of this geometric diagram is:As shown in the figure, in ABCD, given that AC = 4cm, if the perimeter of △ACD is 14cm, then the perimeter of ABCD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

20cm

179

<image>The Caption of this geometric diagram is:As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is α, AC ⊥ CD, BD ⊥ CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac{20}{3}

186

<image>The Caption of this geometric diagram is:As shown in the figure, the diameter CD of ⊙O crosses the midpoint G of chord EF, ∠DCF = 20.0, then ∠EOD is equal to ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

192

<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, points C and D are on ⊙O, ∠BCD = 25°, then the degree measure of ∠AOD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

130°

195

<image>The Caption of this geometric diagram is:As shown in the figure, in △ABC, points D, E, and F are the midpoints of sides BC, AD, and CE respectively, and S△ABC = 4 cm². Then S△DEF equals ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

0.5cm2

196

<image>The Caption of this geometric diagram is:As shown in the figure, in a 5×4 square grid, the side length of each small square is 1, and the vertices of triangle ABC are all at the vertices of these small squares. The value of tan∠BAC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac{4}{3}

203

<image>The Caption of this geometric diagram is:Find the scale factor from point Q to point Q'.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

3

206

<image>The Caption of this geometric diagram is:As shown in the figure, ⊙O is the circumscribed circle of the quadrilateral ABCD, if ∠O = 110.0, then the degree of ∠C is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

125°

220

<image>The Caption of this geometric diagram is:As shown in the figure, A, B, C are three points on ⊙O, ∠ACB = 25.0, then the degree of ∠BAO is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

65°

221

<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of circle O, DB and DC are respectively tangent to circle O at points B and C. If ∠ACE = 25.0, then the degree of ∠D is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

50°

228

<image>The Caption of this geometric diagram is:In the figure shown above, AC = 6. What is the length of segment AB?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

234

<image>The Caption of this geometric diagram is:Find the value of $z$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

12

236

<image>The Caption of this geometric diagram is:Find the length of line segment PTPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac { 20 } { 3 }

238

<image>The Caption of this geometric diagram is:Find the measure of \angle A of quadrilateral ABCDPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

135

242

<image>The Caption of this geometric diagram is:The area $A$ of the shaded region is given. Find the value of $x$. $A = 66$ cm$^2$ .Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

13.0

250

<image>The Caption of this geometric diagram is:As shown in the figure, ∠BAC = 110.0, if A and B are symmetrical with respect to the line MP, A and C are symmetrical with respect to the line NQ, then the size of ∠PAQ is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

255

<image>The Caption of this geometric diagram is:As shown in the figure, in triangle ABC, AD bisects ∠BAC and intersects BC at point D. DE⊥AB with the foot at E. If DE = 3 and AC = 4, then the area of triangle ADC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

256

<image>The Caption of this geometric diagram is:Construct squares outwardly on the three sides of a right triangle. The areas of two of the squares are shown in the figure. Find the area of square A ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

257

<image>The Caption of this geometric diagram is:As shown in the figure, the elevation angle of the top of a building is 30.0 when viewed from point A in the air by a hot air balloon, and the depression angle of this building is 60.0. The horizontal distance between the hot air balloon and the building is 120.0. The height of this building is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

160√{3}m

269

<image>The Caption of this geometric diagram is:As shown in the figure, points A and B are three points on ⊙O and AB = AC. Connect BO and CO, if ∠ABC = 65.0, then the degree of ∠BOC is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

100°

270

<image>The Caption of this geometric diagram is:Find the value of yPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

5

271

<image>The Caption of this geometric diagram is:One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

26

273

<image>The Caption of this geometric diagram is:As shown in the figure, AB, BC, CD, and DA are all tangents to the circle O. Given that AD = 2 and BC = 5, the value of AB + CD is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

7

274

<image>The Caption of this geometric diagram is:As shown in the figure, in Rt△ABC, ∠BAC = 90.0, AD ⊥ BC at D, DE ⊥ AB at E, AD = 3.0, DE = 2.0, then the length of CD is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac{3√{5}}{2}

275

<image>The Caption of this geometric diagram is:As shown in the figure, it is known that the radius of ⊙O is 5.0 and the chord AB = 8.0, then the distance from the center O to AB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

3mm

276

<image>The Caption of this geometric diagram is:In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

60

280

<image>The Caption of this geometric diagram is:$arc XWY \cong arc XYT$. Find the value of $x$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

5

283

<image>The Caption of this geometric diagram is:As shown in the figure, it is known that AB is the diameter of ⊙O, if the degree of ∠BOC is 50.0, then the degree of ∠A is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

25°

285

<image>The Caption of this geometric diagram is:As shown in the figure, an elastic rubber band AB with a length of 8 cm is fixed at both ends on a horizontal table. Then, the midpoint C of the rubber band is pulled vertically upward by 3 cm to point D. At this point, the elastic rubber band is stretched by ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2cm

286

<image>The Caption of this geometric diagram is:As shown in the figure, parallel lines AB and CD are intersected by line AE. If ∠1 = 105°, then the degree measure of ∠2 is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

75°

290

<image>The Caption of this geometric diagram is:${HK}$ and ${IG}$ are diameters of $\odot L$. Find the $measure of arc {LIJ}$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

270

300

<image>The Caption of this geometric diagram is:The Caption of this geometric diagram is:${HK}$ and ${IG}$ are diameters of $\odot L$. Find the $measure of arc {LIJ}$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

100

304

<image>The Caption of this geometric diagram is:Find the value of zPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac { 40 } { 3 }

310

<image>The Caption of this geometric diagram is:In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

125*a^2 + 250

315

<image>The Caption of this geometric diagram is:As shown in the figure, given that points A, B, and C are on ⊙O, ∠AOB = 100.0, then the degree of ∠ACB is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

50°

316

<image>The Caption of this geometric diagram is:Find the area of the figure. Round to the nearest tenth if necessary.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2256

318

<image>The Caption of this geometric diagram is:As shown in the figure, in triangle ABC, ∠C = 90°, AB = 13, AC = 5. D and E are the midpoints of AC and AB respectively. The length of DE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

320

<image>The Caption of this geometric diagram is:As shown in the figure, points A and B are separated by a pond. A point C is chosen outside AB such that point C can directly reach points A and B. Connect AC and BC, and find the midpoints M and N of AC and BC, respectively. If the measured length of MN is 20 m, then the distance between points A and B is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40m

322

<image>The Caption of this geometric diagram is:Find the value of tan(X)Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

\frac { 5 } { 12 }

333

<image>The Caption of this geometric diagram is:In triangle ABC above, AB = AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

8

338

<image>The Caption of this geometric diagram is:As shown in the figure, in ⊙O, AB = AC, ∠BAC = 70°, then the degree measure of ∠AEC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

55°

339

<image>The Caption of this geometric diagram is:In the figure above, which of the following is the greatest?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

d

342

<image>The Caption of this geometric diagram is:As shown in the figure, the parallel lines a and b are intercepted by the straight line c. If ∠1 = 50.0, then the degree of ∠2 is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

130°

355

<image>The Caption of this geometric diagram is:If $\frac{IJ}{XJ}=\frac{HJ}{YJ}, measure of \angle WXJ=130$ and $measure \angle WZG=20,$ find the measure of \angle YIZPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

50

360

<image>The Caption of this geometric diagram is:As shown in the figure, AB is the diameter of ⊙O, and points C and D are on ⊙O. If ∠ABD = 50.0, then the degree of ∠BCD is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

364

<image>The Caption of this geometric diagram is:As shown in the figure, in the right triangle ABC, ∠ABC = 90°, points D, E, and F are the midpoints of sides AB, BC, and CA respectively. If DE + BF = 8, then the value of BF is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

4

371

<image>The Caption of this geometric diagram is:As shown in the figure, in the quadrilateral ABCD, ∠BAD = 120.0, ∠B = ∠D = 90.0, if you find a point M on BC and CD respectively, so that the perimeter of △AMN is the smallest, then the degree of ∠AMN + ∠ANM is ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

120°

373

<image>The Caption of this geometric diagram is:Find the length of $AC$ in the isosceles triangle ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

7

375

<image>The Caption of this geometric diagram is:As shown in the figure, AD is the midline of triangle ABC, E is the midpoint of AD, and the area of triangle ABE is 2. Then the area of triangle ABC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

8

378

<image>The Caption of this geometric diagram is:Find the value of xPlease provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

10 \sqrt { 3 }

386

<image>The Caption of this geometric diagram is:Express the ratio of $\tan M$ as a decimal to the nearest hundredth.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

0.42

388

<image>The Caption of this geometric diagram is:As shown in the figure, point O is the center of ⊙O, points A, B, and C are on ⊙O, AO ∥ BC, ∠AOB = 40.0, then the degree of ∠OAC is equal to ()Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

20°

391

<image>The Caption of this geometric diagram is:As shown in the figure, points A, B, and C are all on ⊙O with a radius of 2, and ∠C＝30°. Find the length of chord AB.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2

397

<image>The Caption of this geometric diagram is:What is the perimeter of the shape?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6

399

<image>The Caption of this geometric diagram is:Find the length of TX if $E X=24$ and $D E=7$Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

32

403

<image>The Caption of this geometric diagram is:As shown in the figure, points B, D, E, and C lie on the same straight line. If △ABD ≌ △ACE and ∠AEC = 110°, then the measure of ∠DAE is ( ).Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

407

<image>The Caption of this geometric diagram is:Find the value of z.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

6 \sqrt { 5 }

408

<image>The Caption of this geometric diagram is:Find the perimeter of $\triangle DEF,$ if $\triangle DEF \sim \triangle CBF,$ perimeter of $\triangle CBF=27, DF=6,$ and $FC=8$Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

20.25

410

<image>The Caption of this geometric diagram is:Given: As shown in the figure, in triangle ABC, AB = AC, BD is the bisector of ∠ABC, and ∠BDC = 75°. Find the degree measure of ∠A.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

40°

413

<image>The Caption of this geometric diagram is:If $ST=8, TR=4$, and $PT=6$, find the length of $QR$.Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

9

414

<image>The Caption of this geometric diagram is:In a right triangle ABC, ∠C = 90°, if AC = 6 and BC = 8, then the value of cos A is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

0.6

425

<image>The Caption of this geometric diagram is:As shown in the figure, if DE is the midline of △ABC and the perimeter of △ADE is 1, then the perimeter of △ABC is ().Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

2

426

<image>The Caption of this geometric diagram is:In the figure above, side AC of triangle ABC is on line l. What is x in terms of k?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

60-k

434

<image>The Caption of this geometric diagram is:What is the perimeter of the shape?Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption. You first think within <think></think> tags and then provide all CDLs within <CDL></CDL> tags.

9

441