images
listlengths 1
1
| problem
stringlengths 14
343
| answer
stringlengths 1
103
| id
int64 91
70k
| choices
null | ground_truth
stringlengths 1
103
|
|---|---|---|---|---|---|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2840.jpg"
}
] |
<image>如图,已知AB∥DE,∠ABC=70°,∠CDE=140°,则∠BCD的值为()
Choices:
(A) 20°
(B) 30°
(C) 40°
(D) 70°
|
30°
| 31,319 | null |
30°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2906.jpg"
}
] |
<image>如图,在▱APBC中,∠C=40°,若⊙O与PA、PB相切于点A、B,则∠CAB=()
Choices:
(A) 40°
(B) 50°
(C) 60°
(D) 70°
|
70°
| 31,385 | null |
70°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2934.jpg"
}
] |
<image>如图,AB是⊙O的直径,BC是⊙O的弦,CD切⊙O于点C,∠D=90°,∠A=60°,则∠C等于()
Choices:
(A) 165°
(B) 150°
(C) 135°
(D) 120°
|
150°
| 31,413 | null |
150°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2947.jpg"
}
] |
<image>把直尺、三角尺和圆形螺母按如图所示放置于桌面上,∠CAB=60°,若量出AD=6cm,则圆形螺母的外直径是()
Choices:
(A) 12cm
(B) 24cm
(C) 6√{3}cm
(D) 12√{3}cm
|
12√{3}cm
| 31,426 | null |
12√{3}cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2958.jpg"
}
] |
<image>如图,AB是⊙O的直径,直线DA与⊙O相切于点A,DO交⊙O于点C,连接BC,若∠ABC=21°,则∠ADC的度数为()
Choices:
(A) 46°
(B) 47°
(C) 48°
(D) 49°
|
48°
| 31,437 | null |
48°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2967.jpg"
}
] |
<image>如图,在△ABC中,∠B=20°,点O是BC边上一点,以O为圆心,OB为半径作圆,交AB边于点D,连结CD,若CD恰好与⊙O相切,则∠DCB的度数是()
Choices:
(A) 30°
(B) 40°
(C) 45°
(D) 50°
|
50°
| 31,446 | null |
50°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2971.jpg"
}
] |
<image>在Rt△ABC中,∠C=90°,AC=10,BC=12,点D为线段BC上一动点．以CD为⊙O直径,作AD交⊙O于点E,连BE,则BE的最小值为()
Choices:
(A) 6
(B) 8
(C) 10
(D) 12
|
8
| 31,450 | null |
8
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2989.jpg"
}
] |
<image>如图,AB是⊙O的直径,直线PA与⊙O相切于点A,PO交⊙O于点C,连接BC．若∠ABC=25°,则∠P的度数为()
Choices:
(A) 50°
(B) 40°
(C) 65°
(D) 55°
|
40°
| 31,468 | null |
40°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3023.jpg"
}
] |
<image>如图,AB是⊙O的直径,C是⊙O上的点,过点C作⊙O的切线交AB的延长线于点E,若∠A=30°,则sin∠E的值为()
Choices:
(A) \frac{1}{2}
(B) \frac{√{2}}{2}
(C) \frac{√{3}}{2}
(D) \frac{√{3}}{3}
|
\frac{√{2}}{2}
| 31,502 | null |
\frac{√{2}}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3045.jpg"
}
] |
<image>如图,直线AB、AD分别与⊙O切于点B、D,C为⊙O上一点,且∠BCD=132°,则∠A的度数是()
Choices:
(A) 48°
(B) 84°
(C) 90°
(D) 96°
|
84°
| 31,524 | null |
84°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3204.jpg"
}
] |
<image>如图,已知点M为平行四边形ABCD边AB的中点,线段CM交BD于点E,S△BEM=2,则图中阴影部分的面积为()
Choices:
(A) 5
(B) 4
(C) 8
(D) 6
|
8
| 31,683 | null |
8
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3238.jpg"
}
] |
<image>如图,已知a∥b∥c,AC=6,AB=2,EF=5,则DF的值为()
Choices:
(A) \frac{5}{3}
(B) \frac{5}{2}
(C) \frac{10}{3}
(D) \frac{15}{2}
|
\frac{15}{2}
| 31,717 | null |
\frac{15}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3301.jpg"
}
] |
<image>如图,在平行四边形ABCD中,E为AB的中点,F为AD上一点,EF交AC于G,AF=2cm,DF=4cm,AG=3cm,则AC的长为()
Choices:
(A) 9cm
(B) 14cm
(C) 15cm
(D) 18cm
|
15cm
| 31,780 | null |
15cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3366.jpg"
}
] |
<image>如图,已知直线a∥b∥c,分别交直线m、n于点A、C、E、B、D、F,AC=4,CE=6,BD=3,则BF的长为()
Choices:
(A) \frac{9}{2}
(B) \frac{15}{2}
(C) 6
(D) \frac{5}{2}
|
\frac{15}{2}
| 31,845 | null |
\frac{15}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3380.jpg"
}
] |
<image>如图,已知AD为△ABC的角平分线,DE∥AB交AC于E,如果\frac{AE}{EC}=\frac{3}{5},那么\frac{AC}{AB}等于()
Choices:
(A) \frac{3}{5}
(B) \frac{5}{3}
(C) \frac{8}{5}
(D) \frac{3}{2}
|
\frac{5}{3}
| 31,859 | null |
\frac{5}{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3392.jpg"
}
] |
<image>如图,在四边形ABCD中,∠A=110°,∠B=85°将△BMN沿着MN翻折,得到△FMN,若MF∥AD,FN∥DC,则∠C的度数为()
Choices:
(A) 70°
(B) 80°
(C) 90°
(D) 100°
|
80°
| 31,871 | null |
80°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3408.jpg"
}
] |
<image>如图,在梯形ABCD中,AD∥BC,E、F分别是对角线BD、AC的中点,若AD=6cm,BC=18cm,则EF的长为()
Choices:
(A) 8cm
(B) 7cm
(C) 6cm
(D) 5cm
|
6cm
| 31,887 | null |
6cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3420.jpg"
}
] |
<image>如图,直线a∥b∥c,且a,b之间的距离为1,△ABC和△CDE是两块全等的直角三角形纸板,其中∠ABC=∠CDE=90°,∠BAC=∠DCE=30°,它们的顶点都在平行线上,则b,c之间的距离是()
Choices:
(A) 1
(B) √{2}
(C) √{3}
(D) 2
|
√{3}
| 31,899 | null |
√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3422.jpg"
}
] |
<image>如图,一把带有60°角的三角尺放在两条平行线间,已知量得平行线间的距离为12cm,三角尺最短边和平行线成45°角,则三角尺斜边的长度为()
Choices:
(A) 12cm
(B) 12√{2}cm
(C) 24cm
(D) 24√{2}cm
|
24√{2}cm
| 31,901 | null |
24√{2}cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3429.jpg"
}
] |
<image>如图,将一个直角三角形纸片ABC,沿线段CD折叠,使点B落在B′处,若∠ACB′=72°,则∠ACD的度数为()
Choices:
(A) 9°
(B) 10°
(C) 12°
(D) 18°
|
9°
| 31,908 | null |
9°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3488.jpg"
}
] |
<image>如图所示,P是⊙O的弦AB上的一点,AB=10cm,AP=4cm,OP=5cm,则⊙O的半径为cm．()
Choices:
(A) 5
(B) 7
(C) 6
(D) 6.5
|
7
| 31,967 | null |
7
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3496.jpg"
}
] |
<image>如图,AB是⊙O的弦,OC⊥AB于H,∠AOC=60°,OH=1,则⊙O的半径为()
Choices:
(A) √{3}
(B) 2
(C) 3
(D) 4
|
4
| 31,975 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3529.jpg"
}
] |
<image>如图在灯塔O处观测到轮船A位于北偏西56°的方向,同时轮船B在南偏东17°的方向,那么∠AOB的大小为()
Choices:
(A) 159°
(B) 141°
(C) 111°
(D) 69°
|
141°
| 32,008 | null |
141°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3600.jpg"
}
] |
<image>如图,两条直线被三条平行线所截,若AC=4,CE=6,BD=3,则BF=()
Choices:
(A) \frac{3}{2}
(B) \frac{2}{3}
(C) \frac{9}{2}
(D) \frac{15}{2}
|
\frac{15}{2}
| 32,079 | null |
\frac{15}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3695.jpg"
}
] |
<image>如图,△ABC中,CA=CB,AB=9cm,点D在AC上,AD=3cm．将线段AD沿着AB的方向平移5cm得到线段MN,点M落在边CB,点N落在边AB上,则△BMN的周长为()
Choices:
(A) 17cm
(B) 15cm
(C) 11cm
(D) 10cm
|
10cm
| 32,174 | null |
10cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3696.jpg"
}
] |
<image>如图,在▱ABCD中,AE平分∠BAD,已知∠AEB=63°,则∠D的度数为()
Choices:
(A) 63°
(B) 72°
(C) 54°
(D) 60°
|
54°
| 32,175 | null |
54°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3735.jpg"
}
] |
<image>如图,把一个含30°角的直角三角尺的直角顶点放在直尺的一边上,如果∠1=20°,那么∠2的度数为()
Choices:
(A) 20°
(B) 50°
(C) 60°
(D) 70°
|
50°
| 32,214 | null |
50°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3736.jpg"
}
] |
<image>如图,在▱ABCD中,点E、F分别在CD、BC的延长线上,AE∥BD,EF⊥BF,∠ABC=60°,EF=3,则AB的长是()
Choices:
(A) \frac{2}{3}
(B) 1
(C) \frac{3}{2}
(D) √{3}
|
√{3}
| 32,215 | null |
√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3740.jpg"
}
] |
<image>如图,在▱ABCD中,AB=18,AD=12,∠ABC的平分线交CD于点F,交AD的延长线于点E,CG⊥BE,垂足为G,若EF=4,则线段CG的长为()
Choices:
(A) 2√{35}
(B) 6√{3}
(C) 4√{10}
(D) 8√{2}
|
8√{2}
| 32,219 | null |
8√{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3743.jpg"
}
] |
<image>如图,已知点M为▱ABCD边AB的中点,线段CM交BD于点E,S~△BEM~=1,则图中阴影部分的面积为()
Choices:
(A) 2
(B) 3
(C) 4
(D) 5
|
4
| 32,222 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3793.jpg"
}
] |
<image>如图,将边长为5个单位长度的等边△ABC沿边BC向右平移4个单位得到△A′B′C′,则线段B′C的长为()
Choices:
(A) 1
(B) 2
(C) 4
(D) 5
|
4
| 32,272 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3796.jpg"
}
] |
<image>如图,在△ABC中,AB=AC,BD=\frac{9}{4}BC,等边△BEF的顶点F在BC上,边EF交AD于点P,若BE=10,BC=14,则PE的长为()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 32,275 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3813.jpg"
}
] |
<image>如图,在△ABC中,点D、E分别是边AB、AC上的点,DE垂直平分AB,∠C=90°,∠BAC=15°．若BC=3cm,则AE的长度为()
Choices:
(A) 9cm
(B) 6cm
(C) 5cm
(D) 4cm
|
6cm
| 32,292 | null |
6cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3836.jpg"
}
] |
<image>如图,在Rt△ABC中,∠ACB=90°,AC=6,BC=8,AD是∠BAC的平分线．若P,Q分别是AD和AC上的动点,则PC+PQ的最小值是()
Choices:
(A) \frac{12}{5}
(B) 4
(C) \frac{24}{5}
(D) 5
|
\frac{24}{5}
| 32,315 | null |
\frac{24}{5}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3858.jpg"
}
] |
<image>如图,在▱ABCD中,用直尺和圆规作∠BAD的平分线AG交BC于点E,若BF=12,AB=10,则AE的长为()
Choices:
(A) 8
(B) 12
(C) 16
(D) 20
|
16
| 32,337 | null |
16
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3861.jpg"
}
] |
<image>如图,在▱ABCD中,∠ODA=90°,AC=10cm,BD=6cm,则BC的长为()
Choices:
(A) 4cm
(B) 5cm
(C) 6cm
(D) 8cm
|
4cm
| 32,340 | null |
4cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3874.jpg"
}
] |
<image>在△ABC中,点M为BC的中点,AD平分∠BAC,且BD⊥AD于点D,延长BD交AC于点N若AB=4,DM=1,则AC的长为()
Choices:
(A) 5
(B) 6
(C) 7
(D) 8
|
6
| 32,353 | null |
6
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3937.jpg"
}
] |
<image>如图,PA、PB是半径为1的⊙O的两条切线,点A、B分别为切点,∠APB=60°,OP与弦AB交于点C,与⊙O交于点D．则图中阴影部分的面积是()
Choices:
(A) \frac{1}{3}π
(B) \frac{1}{3}π-\frac{√{3}}{4}
(C) \frac{1}{6}π
(D) \frac{1}{6}π-\frac{√{3}}{4}
|
\frac{1}{6}π
| 32,416 | null |
\frac{1}{6}π
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4046.jpg"
}
] |
<image>如图,某校A与公路距离为3000米,又与该公路旁上的某车站D的距离为5000米,现要在公路边建一个商店C,使之与该校A及车站D的距离相等,则商店与车站的距离约为()
Choices:
(A) 875米
(B) 3125米
(C) 3500米
(D) 3275米
|
3125米
| 32,525 | null |
3125米
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4132.jpg"
}
] |
<image>如图,点A、B、C在圆O的圆周上,连OA、OC,OD⊥AB于点D,若AO平分∠CAB,∠CAB=50°,则∠OCB=()
Choices:
(A) 40°
(B) 35°
(C) 30°
(D) 25°
|
40°
| 32,611 | null |
40°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4145.jpg"
}
] |
<image>如图,等边△ABC的边长为3,P为BC上一点,且BP=1,D为AC上一点,若∠APD=60°,则CD的长是()
Choices:
(A) \frac{4}{5}
(B) \frac{3}{4}
(C) \frac{2}{3}
(D) \frac{1}{2}
|
\frac{2}{3}
| 32,624 | null |
\frac{2}{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4159.jpg"
}
] |
<image>如图,四边形ABCD中,AB=4,BC=6,AB⊥BC,BC⊥CD,E为AD的中点,F为线段BE上的点,且FE=\frac{1}{3}BE,则点F到边CD的距离是()
Choices:
(A) 3
(B) \frac{10}{3}
(C) 4
(D) \frac{14}{3}
|
4
| 32,638 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4216.jpg"
}
] |
<image>如图,在△ABC中,∠BAC=90°,AB=20,AC=15,△ABC的高AD与角平分线CF交于点E,则\frac{DE}{AF}的值为()
Choices:
(A) \frac{3}{5}
(B) \frac{3}{4}
(C) \frac{1}{2}
(D) \frac{2}{3}
|
\frac{3}{5}
| 32,695 | null |
\frac{3}{5}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4245.jpg"
}
] |
<image>如图,在平行四边形ABCD中,E为AD的中点,△DEF的周长为1,则△BCF的周长为()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 32,724 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4258.jpg"
}
] |
<image>如图,在▱ABCD中,AE=EB,AF=2,则FC等于()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 32,737 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4300.jpg"
}
] |
<image>如图,量角器上有40°和60°两个刻度点C、D,O是原点,OB是0刻度线,那么∠DAC的度数是()
Choices:
(A) 10°
(B) 12°
(C) 15°
(D) 20°
|
10°
| 32,779 | null |
10°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4322.jpg"
}
] |
<image>如图,已知四边形ABCD内接于⊙O,直径AC=6,对角线AC、BD交于E点,且AB=BD,EC=1,则AD的长为()
Choices:
(A) \frac{3√{15}}{2}
(B) \frac{17}{3}
(C) \frac{11}{2}
(D) 3√{2}
|
\frac{3√{15}}{2}
| 32,801 | null |
\frac{3√{15}}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4327.jpg"
}
] |
<image>如图,已知D、E、F分别为等腰△ABC边BC、CA、AB上的点,如果AB=AC,∠FDE=∠B,BD=2,CD=3,CE=4,AE=1,那么AF的长为()
Choices:
(A) 3.5
(B) 4
(C) 4.5
(D) 5
|
3.5
| 32,806 | null |
3.5
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4376.jpg"
}
] |
<image>如图,四边形ABCD是矩形,点E和点F是矩形ABCD外两点,AE⊥CF于点H,AD=3,DC=4,DE=\frac{5}{2},∠EDF=90°,则DF长是()
Choices:
(A) \frac{15}{8}
(B) \frac{11}{3}
(C) \frac{10}{3}
(D) \frac{16}{5}
|
\frac{10}{3}
| 32,855 | null |
\frac{10}{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4378.jpg"
}
] |
<image>如图,半径为5的⊙A中,弦BC,ED所对的圆心角分别是∠BAC,∠EAD,已知DE=6,∠BAC+∠EAD=180°,则弦BC的长等于()
Choices:
(A) √
(B) √
(C) 8
(D) 6
|
8
| 32,857 | null |
8
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4389.jpg"
}
] |
<image>如图,菱形ABCD和菱形ECGF,且B、C、G共线,若菱形ABCD和菱形ECGF的边长分别为4和6,∠A=120°,则图中阴影部分的面积是()
Choices:
(A) √{3}
(B) 4
(C) 2√{3}
(D) 4√{3}
|
4√{3}
| 32,868 | null |
4√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4417.jpg"
}
] |
<image>如图所示,在平行四边形ABCD中,CE是∠DCB的平分线,且交AB于E,DB与CE相交于O,已知AB=6,BC=4,则\frac{OB}{DB}等于()
Choices:
(A) \frac{1}{3}
(B) \frac{2}{5}
(C) \frac{3}{7}
(D) 不一定
|
\frac{2}{5}
| 32,896 | null |
\frac{2}{5}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4451.jpg"
}
] |
<image>如图,已知AB=AC=AD,∠CBD=2∠BDC,∠BAC=42°,则∠CAD的度数为()
Choices:
(A) 110°
(B) 88°
(C) 84°
(D) 66°
|
84°
| 32,930 | null |
84°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/7.jpg"
}
] |
<image>If A D = 27, A B = 8, and A E = 12, find B C.
|
B
| 32,942 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/58.jpg"
}
] |
<image>Find the measure of \angle R to the nearest tenth.
|
D
| 32,993 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/61.jpg"
}
] |
<image>Equilateral pentagon P Q R S T is inscribed in \odot U. Find m \angle P T S.
|
D
| 32,996 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/74.jpg"
}
] |
<image>W X Y Z is a square. If W T = 3. Find X Y.
|
B
| 33,009 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/90.jpg"
}
] |
<image>Find m \angle 2.
|
C
| 33,025 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/101.jpg"
}
] |
<image>In the figure, \triangle A B C is isosceles, \triangle D C E is equilateral, and \triangle F C G is isosceles. Find the measure of the \angle 3 at vertex C.
|
B
| 33,036 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/125.jpg"
}
] |
<image>Find m \angle 2.
|
B
| 33,060 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/213.jpg"
}
] |
<image>Find y.
|
B
| 33,148 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/216.jpg"
}
] |
<image>Find x.
|
C
| 33,151 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/222.jpg"
}
] |
<image>A B C D is a rhombus. If P B = 12, A B = 15, and m \angle A B D = 24. Find m \angle A C B.
|
D
| 33,157 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/244.jpg"
}
] |
<image>In \odot F, G K = 14 and m \widehat G H K = 142. Find m \widehat K M.
|
B
| 33,179 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/254.jpg"
}
] |
<image>If C E = t - 2. E B = t + 1, C D = 2, and C A = 10, find t.
|
C
| 33,189 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/316.jpg"
}
] |
<image>If R T = 15, Q P = 21, and P T = 8, find T S.
|
C
| 33,251 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/419.jpg"
}
] |
<image>Find the height of the parallelogram given its area with 100 square units.
|
A
| 33,354 | null |
A
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/430.jpg"
}
] |
<image>Use parallelogram M N P R to find m \angle N R P.
|
A
| 33,365 | null |
A
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/525.jpg"
}
] |
<image>\triangle M H J \cong \triangle P Q J. Find y.
|
C
| 33,460 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/545.jpg"
}
] |
<image>Find the measure of \angle 1 if m \angle 4 = m \angle 5.
|
C
| 33,480 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/634.jpg"
}
] |
<image>Find B D.
|
C
| 33,569 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/656.jpg"
}
] |
<image>Find m \angle 4.
|
D
| 33,591 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/677.jpg"
}
] |
<image>If F K = 3 x - 1, K G = 4 y + 3, J K = 6 y - 2, and K H = 2 x + 3, find y so that the quadrilateral is a parallelogram.
|
B
| 33,612 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/690.jpg"
}
] |
<image>Find m \angle T Q R.
|
C
| 33,625 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/778.jpg"
}
] |
<image>Find x.
|
C
| 33,713 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/853.jpg"
}
] |
<image>If m \angle A E D = 95 and m \widehat A D = 120, what is m \angle B A C?
|
B
| 33,788 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/884.jpg"
}
] |
<image>Rhombus R S T U has an area of 675 square meters. Find S U.
|
D
| 33,819 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/887.jpg"
}
] |
<image>A B C D is a rhombus. If E B = 9, A B = 12 and m \angle A B D = 55. Find A E.
|
A
| 33,822 | null |
A
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/902.jpg"
}
] |
<image>Use parallelogram J K L M to find m \angle J M L.
|
C
| 33,837 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1023.jpg"
}
] |
<image>What is the value of x if m \widehat N R = 62 and m \widehat N P = 108?
|
C
| 33,958 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1060.jpg"
}
] |
<image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find M L.
|
C
| 33,995 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1062.jpg"
}
] |
<image>If \frac { I J } { X J } = \frac { H J } { Y J }, m \angle W X J = 130 and m \angle W Z G = 20, find m \angle J H I.
|
B
| 33,997 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1078.jpg"
}
] |
<image>Find m \angle 4.
|
C
| 34,013 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1083.jpg"
}
] |
<image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find K M.
|
B
| 34,018 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1113.jpg"
}
] |
<image>If A C = 14, B C = 8, and A D = 21, find E D.
|
B
| 34,048 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1136.jpg"
}
] |
<image>Find A B.
|
C
| 34,071 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1157.jpg"
}
] |
<image>P Q is tangent to the circle. Find x. Round to the nearest tenth.
|
B
| 34,092 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1172.jpg"
}
] |
<image>Find x so that the quadrilateral is a parallelogram.
|
B
| 34,107 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1179.jpg"
}
] |
<image>R P = 3.5 and J P = 9. Find P S.
|
B
| 34,114 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1210.jpg"
}
] |
<image>Triangle A D C is circumscribed about \odot O. Find the perimeter of \triangle A D C if E C = D E + A F.
|
D
| 34,145 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1223.jpg"
}
] |
<image>Find x. Assume that any segment that appears to be tangent is tangent.
|
A
| 34,158 | null |
A
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1227.jpg"
}
] |
<image>In \odot R, S U = 20, Y W = 20, and m \widehat Y X = 45. Find m \widehat S U.
|
D
| 34,162 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1239.jpg"
}
] |
<image>Find x.
|
B
| 34,174 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1245.jpg"
}
] |
<image>If the perimeter of square 2 is 200 units and the perimeter of square 1 is 150 units, what is the perimeter of square 3?
|
B
| 34,180 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1259.jpg"
}
] |
<image>Find the measure of \angle 4 if m \angle D G F = 53 and m \angle A G C = 40.
|
B
| 34,194 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1263.jpg"
}
] |
<image>In \odot P, J K = 10 and \widehat J K L = 134. Find P Q. Round to the nearest hundredth.
|
B
| 34,198 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1277.jpg"
}
] |
<image>If A B = 8, K L = 10, and J B = 13, find J L.
|
D
| 34,212 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1301.jpg"
}
] |
<image>Use parallelogram A B C D to find m \angle B C D.
|
D
| 34,236 | null |
D
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1390.jpg"
}
] |
<image>Find the perimeter of parallelogram A B C D to the nearest tenth.
|
C
| 34,325 | null |
C
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/1422.jpg"
}
] |
<image>Find A E if A B = 12, A C = 16, and E D = 5.
|
B
| 34,357 | null |
B
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.