images
listlengths 1
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stringlengths 14
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| choices
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stringlengths 1
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|---|---|---|---|---|---|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3264.jpg"
}
] |
<image>如图,l1∥l2∥l3,AB=3,BC=2,EF=3,则DF的长为()
Choices:
(A) 3
(B) 5.5
(C) 6.5
(D) 7.5
|
7.5
| 31,743 | null |
7.5
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3277.jpg"
}
] |
<image>如图,在△ABC中,DE∥BC,DF∥AC,EG∥AB,且AE:EC=3:2,若BC=10,则FG的长为()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 31,756 | null |
4
|
[
{
"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/3352.jpg"
}
] |
<image>如图,△OED∽△OCB,且OE=6,EC=21,则△OCB与△OED的相似比是()
Choices:
(A) \frac{3}{7}
(B) \frac{5}{2}
(C) \frac{8}{5}
(D) \frac{3}{5}
|
\frac{5}{2}
| 31,831 | null |
\frac{5}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3360.jpg"
}
] |
<image>如图,△ABC中,∠ABD=∠C,若AB=4,AD=2,则CD边的长是()
Choices:
(A) 2
(B) 4
(C) 6
(D) 8
|
6
| 31,839 | null |
6
|
[
{
"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/3382.jpg"
}
] |
<image>如图,AD∥BE∥CF,直线l1、l2与这三条平行线分别交于点A、B、C和点D、E、F,若AB=3,BC=6,DF=6,则DE的长等于()
Choices:
(A) 2
(B) 3
(C) 4
(D) 6
|
4
| 31,861 | null |
4
|
[
{
"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/3407.jpg"
}
] |
<image>如图,在△ABC中,∠ABC=90°,∠A=30°,BC=4．若DE是△ABC的中位线,延长DE交∠ACM的平分线于点F,则DF的长为()
Choices:
(A) 6
(B) 7
(C) 8
(D) 9
|
6
| 31,886 | null |
6
|
[
{
"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/3430.jpg"
}
] |
<image>如图,在四边形ABCD中,∠DAB的角平分线与∠ABC的外角平分线相交于点P,且∠D+∠C=210°,则∠P=()
Choices:
(A) 10°
(B) 15°
(C) 30°
(D) 40°
|
15°
| 31,909 | null |
15°
|
[
{
"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/3505.jpg"
}
] |
<image>如图,图①是一个四边形纸条ABCD,其中AB∥CD,E,F分别为边AB,CD上的两个点,将纸条ABCD沿EF折叠得到图②,再将图②沿DF折叠得到图③,若在图③中,∠FEM=26°,则∠EFC的度数为()
Choices:
(A) 52°
(B) 64°
(C) 102°
(D) 128°
|
102°
| 31,984 | null |
102°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3518.jpg"
}
] |
<image>如图,在菱形ABCD中,∠BAD=80°,AB的垂直平分线交对角线AC于点F,点E为垂足,连接DF,则∠CDF为()
Choices:
(A) 80°
(B) 70°
(C) 65°
(D) 60°
|
60°
| 31,997 | null |
60°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3521.jpg"
}
] |
<image>如图:∠A=50°,BP平分∠ABC,DP平分∠ADC,∠P=20°,则∠C=()
Choices:
(A) 20°
(B) 15°
(C) 5°
(D) 10°
|
10°
| 32,000 | null |
10°
|
[
{
"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/3543.jpg"
}
] |
<image>小明把一副直角三角尺按如图所示的方式摆放在一起,其中∠E=90°,∠C=90°,∠A=45°,∠D=30°,则∠1+∠2等于()
Choices:
(A) 120°
(B) 150°
(C) 180°
(D) 210°
|
210°
| 32,022 | null |
210°
|
[
{
"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/3651.jpg"
}
] |
<image>如图,E,F分别为矩形ABCD的边AD,BC的中点,若矩形ABCD与矩形EABF相似,AB=1,则矩形ABCD的面积是()
Choices:
(A) 4
(B) 2
(C) √{3}
(D) √{2}
|
√{2}
| 32,130 | null |
√{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3658.jpg"
}
] |
<image>如图,在▱ABCD中,∠A=65°,DE⊥AB,垂足为点E,点F为边AD上的中点,连接FE,则∠AFE的度数为()
Choices:
(A) 40°
(B) 50°
(C) 60°
(D) 70°
|
50°
| 32,137 | null |
50°
|
[
{
"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/3747.jpg"
}
] |
<image>如图,▱ABCD的对角线AC与BD相交于点O,AC⊥BC,且AB=10,AD=6,则OB的长度为()
Choices:
(A) 2√{13}
(B) 4
(C) 8
(D) 4√{13}
|
2√{13}
| 32,226 | null |
2√{13}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3750.jpg"
}
] |
<image>如图,在平行四边形ABCD中,点E是AB边上一点,连接DE、CE．若DE、CE分别是∠ADC、∠BCD的角平分线,且AB=4,则平行四边形ABCD的周长为()
Choices:
(A) 10
(B) 8√{2}
(C) 5√{5}
(D) 12
|
12
| 32,229 | null |
12
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3759.jpg"
}
] |
<image>如图,已知AE平分∠BAC,BE⊥AE于E,ED∥AC,∠BAE=36°,那么∠BED的度数为()
Choices:
(A) 108°
(B) 120°
(C) 126°
(D) 144°
|
126°
| 32,238 | null |
126°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3773.jpg"
}
] |
<image>如图,四边形ABCD中,AB∥CD,AD∥BC,且∠BAD、∠ADC的角平分线AE、DF分别交BC于点E、F．若EF=2,AB=5,则AD的长为()
Choices:
(A) 7
(B) 6
(C) 8
(D) 9
|
8
| 32,252 | null |
8
|
[
{
"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/3810.jpg"
}
] |
<image>如图,已知∠ACB=60°,PC=12,点M,N在边CB上,PM=PN．若MN=3,则CM的长为()
Choices:
(A) 3
(B) 3.5
(C) 4
(D) 4.5
|
4.5
| 32,289 | null |
4.5
|
[
{
"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/3839.jpg"
}
] |
<image>如图,∠AOB=20°,点M、N分别是边OA、OB上的定点,点P、Q分别是边OB、OA上的动点,记∠MPQ=α,∠PQN=β,当MP+PQ+QN最小时,则β-α的值为()
Choices:
(A) 10°
(B) 20°
(C) 40°
(D) 60°
|
40°
| 32,318 | null |
40°
|
[
{
"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/3871.jpg"
}
] |
<image>已知,如图,在△ABC中,D是BC的中点,AE平分∠BAC,BE⊥AE于点E,且AC=14,ED=3,则AB的长是()
Choices:
(A) 6
(B) 7
(C) 8
(D) 9
|
8
| 32,350 | null |
8
|
[
{
"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/3890.jpg"
}
] |
<image>如图,m∥n,点A在直线n上,以A为圆心的圆弧与直线n,m相交于B,C,若∠CAB=30°,则∠ABC的度数为()
Choices:
(A) 45°
(B) 60°
(C) 70°
(D) 75°
|
75°
| 32,369 | null |
75°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3891.jpg"
}
] |
<image>同学们都玩过跷跷板的游戏,如图是一个跷跷板的示意图,立柱OC与地面垂直,OA=OB．当跷跷板的一头A着地时,∠AOA′=50°,则当跷跷板的另一头B着地时,∠COB′等于()
Choices:
(A) 25°
(B) 50°
(C) 65°
(D) 130°
|
65°
| 32,370 | null |
65°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3902.jpg"
}
] |
<image>如图,在△ABE中,BA=BE,F为AE中点．若∠ABC=34°,∠C=50°,则∠ADB的度数为()
Choices:
(A) 60°
(B) 63°
(C) 67°
(D) 70°
|
67°
| 32,381 | null |
67°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3909.jpg"
}
] |
<image>如图,P为平行四边形ABCD内一点,过点P分别作AB、AD的平行线交平行四边形于E、F、G、H四点,若S~AHPE~=3,S~PFCG~=5,则S~△PBD~为()
Choices:
(A) 1.5
(B) 1
(C) 2.5
(D) 3
|
1
| 32,388 | null |
1
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3912.jpg"
}
] |
<image>如图,▱ABCD中,AB=6,E是BC边的中点,F为CD边上一点,DF=4.8,∠DFA=2∠BAE,则AF的长为()
Choices:
(A) 4.8
(B) 6
(C) 7.2
(D) 10.8
|
7.2
| 32,391 | null |
7.2
|
[
{
"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/3939.jpg"
}
] |
<image>如图,直径为6的半圆绕直径AB的端点A顺时针旋转45°,点B的对应点为B′,则图中阴影部分的面积是()
Choices:
(A) \frac{3}{4}π
(B) \frac{9}{4}π
(C) \frac{9}{2}π
(D) 9π
|
\frac{9}{2}π
| 32,418 | null |
\frac{9}{2}π
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3949.jpg"
}
] |
<image>如图,AC是汽车挡风玻璃前的刮雨刷．如果AO=65cm,CO=15cm,当刮雨刷AC绕点O旋转90°时,则刮雨刷AC扫过的面积为()
Choices:
(A) 25πcm²
(B) 1000πcm²
(C) 25cm²
(D) 1000cm²
|
1000πcm²
| 32,428 | null |
1000πcm²
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4002.jpg"
}
] |
<image>为了测量两岸平行的河宽AB,测得∠ACB=30°,∠ADB=60°,CD=60m,则河宽AB为()
Choices:
(A) 30m
(B) 30√{3}m
(C) (30√{3}+30)m
(D) (30√{3}-30)m
|
30√{3}m
| 32,481 | null |
30√{3}m
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4008.jpg"
}
] |
<image>如图,为了测量河的宽度,王芳同学在河岸边相距200m的M和N两点分别测定对岸一棵树P的位置,P在M的正北方向,在N的北偏西30°的方向,则河的宽度是()
Choices:
(A) 200√{3}m
(B) \frac{200√{3}}{3}m
(C) 100√{3}m
(D) 100m
|
200√{3}m
| 32,487 | null |
200√{3}m
|
[
{
"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/4048.jpg"
}
] |
<image>如图,在正方形ABCD中,G为CD边中点,连接AG并延长,分别交对角线BD于点F,交BC边延长线于点E．若FG=2,则AE的长度为()
Choices:
(A) 6
(B) 8
(C) 10
(D) 12
|
12
| 32,527 | null |
12
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4130.jpg"
}
] |
<image>如图所示,在正方形ABCD中,G为CD边中点,连接AG并延长交BC边的延长线于E点,对角线BD交AG于F点．已知FG=2,则线段AE的长度为()
Choices:
(A) 6
(B) 8
(C) 10
(D) 12
|
12
| 32,609 | null |
12
|
[
{
"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/4208.jpg"
}
] |
<image>如图,在▱ABCD中,对角线AC与BD相交于点O,在DC的延长线上取一点E,连接OE交BC于点F．已知AB=4,BC=6,CE=2,则CF的长等于()
Choices:
(A) 1
(B) 1.5
(C) 2
(D) 3
|
1.5
| 32,687 | null |
1.5
|
[
{
"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/4221.jpg"
}
] |
<image>如图,AB是半圆O的直径,∠DBA=20°,则∠C的大小是()
Choices:
(A) 70°
(B) 100°
(C) 110°
(D) 140°
|
110°
| 32,700 | null |
110°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4226.jpg"
}
] |
<image>已知△ABC中,AD∥BC,CD交AB于E,EF∥BC,AE:EB=1:2,S~△ADE~=1,则S~△AEF~=()
Choices:
(A) \frac{1}{3}
(B) \frac{1}{2}
(C) \frac{2}{3}
(D) \frac{3}{4}
|
\frac{2}{3}
| 32,705 | null |
\frac{2}{3}
|
[
{
"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/4265.jpg"
}
] |
<image>如图,平行四边形ABCD中,E为AB中点,F为AD上一点,EF交AC于点G,AF=3cm,DF=6cm,AG=4cm,则AC的长为()
Choices:
(A) 12cm
(B) 16cm
(C) 20cm
(D) 24cm
|
20cm
| 32,744 | null |
20cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4280.jpg"
}
] |
<image>如图,在△ABC中,∠B+∠CDE=∠C+∠BED,AE=2,AD=3,CD=1,则BE等于()
Choices:
(A) \frac{3}{2}
(B) \frac{2}{3}
(C) 2
(D) 4
|
4
| 32,759 | 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/4358.jpg"
}
] |
<image>如图,已知△ABC和△ADE均为等边三角形,D在BC上,DE与AC相交于点F,AB=9,BD=3,则CF等于()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 32,837 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4359.jpg"
}
] |
<image>如图,△ABC中,AB=AC=18,BC=12,正方形DEFG的顶点E,F在△ABC内,顶点D,G分别在AB,AC上,AD=AG,DG=6,则点F到BC的距离为()
Choices:
(A) 1
(B) 2
(C) 12√{2}-6
(D) 6√{2}-6
|
6√{2}-6
| 32,838 | null |
6√{2}-6
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/4363.jpg"
}
] |
<image>如图,AD是△ABC的高,AB=15,AC=12,AD=10,则△ABC的外接圆直径AE长为()
Choices:
(A) 20
(B) 18
(C) 16
(D) 10√{3}
|
18
| 32,842 | null |
18
|
[
{
"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/4377.jpg"
}
] |
<image>如图,已知等边三角形ABC的边长是9,P为BC上一点,且BP=3,D为AC上一点,∠APD=60°,则线段CD的长是()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 32,856 | null |
4
|
[
{
"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/4440.jpg"
}
] |
<image>如图,a//b,Ð1=65°,Ð2=140°,则Ð3=()
Choices:
(A) 100°
(B) 105°
(C) 110°
(D) 115°
|
105°
| 32,919 | null |
105°
|
[
{
"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/38.jpg"
}
] |
<image>Find the measure of \angle 2.
|
A
| 32,973 | null |
A
|
[
{
"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/105.jpg"
}
] |
<image>Find x.
|
D
| 33,040 | null |
D
|
[
{
"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/147.jpg"
}
] |
<image>In \triangle J K L, P T = 2. Find K P.
|
B
| 33,082 | null |
B
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/Geometry3K/150.jpg"
}
] |
<image>If P R \parallel K L, K N = 9, L N = 16, and P M = 2K P, find M L.
|
C
| 33,085 | null |
C
|
[
{
"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/268.jpg"
}
] |
<image>Find the area of the shaded region. Round to the nearest tenth.
|
C
| 33,203 | 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
|
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