images
listlengths 1
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stringlengths 14
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stringlengths 1
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|---|---|---|---|---|---|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1112.jpg"
}
] |
<image>如图,在▱ABCD中,AD=2AB,CE平分∠BCD交AD边于点E,且AE=3,则AB的长为()
Choices:
(A) 4
(B) 3
(C) \frac{5}{2}
(D) 2
|
2
| 29,591 | null |
2
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1153.jpg"
}
] |
<image>如图,经过⊙O上点A的切线和弦BC的延长线相交于点P,若∠CAP=40°,∠ACP=100°,则∠BAC的度数为()
Choices:
(A) 40°
(B) 60°
(C) 80°
(D) 70°
|
60°
| 29,632 | null |
60°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1158.jpg"
}
] |
<image>如图,线段AB过圆心O,交⊙O于点A、C,∠B=30°,直线BD与⊙O切于点D,则∠ADB的度数是()
Choices:
(A) 150°
(B) 135°
(C) 120°
(D) 100°
|
120°
| 29,637 | null |
120°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1159.jpg"
}
] |
<image>如图所示,直线MN与△ABC的外接圆相切于点A,AC平分∠MAB,如果AN=6,NB=4,那么弦AC的长为()
Choices:
(A) 4
(B) 5
(C) 6
(D) 9
|
5
| 29,638 | null |
5
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1160.jpg"
}
] |
<image>如图,在Rt△ABC中,∠BAC=90°,∠ABC=30°,Q是AB上的一点,⊙O分别与AC、BC相切于点A、D,与AB交于另一点E,若BE=2,则切线CD的长为()
Choices:
(A) √{3}
(B) 2√{3}
(C) 3√{3}
(D) 6
|
2√{3}
| 29,639 | null |
2√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1172.jpg"
}
] |
<image>如图AB是⊙O直径,点D在AB延长线上,DC切⊙O于点C,∠A=20°,则∠D的度数为()
Choices:
(A) 20°
(B) 30°
(C) 40°
(D) 50°
|
50°
| 29,651 | null |
50°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1184.jpg"
}
] |
<image>如图,将三角形纸板的直角顶点放在直尺的一边上,∠1=20°,∠2=40°,则∠3等于()
Choices:
(A) 50°
(B) 30°
(C) 20°
(D) 15°
|
20°
| 29,663 | null |
20°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1202.jpg"
}
] |
<image>如图,DC∥AB,∠BAE=∠BCD,AE⊥DE,∠C=130°,则∠D的度数是()
Choices:
(A) 160°
(B) 140°
(C) 130°
(D) 125°
|
140°
| 29,681 | null |
140°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1212.jpg"
}
] |
<image>如图,把平行四边形ABCD分成4个平行四边形,已知其中三个面积分别为8、10、30,则第四个平行四边形的面积是()
Choices:
(A) 28
(B) 26
(C) 24
(D) 22
|
24
| 29,691 | null |
24
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1218.jpg"
}
] |
<image>设BF交AC于点P,AE交DF于点Q．若∠APB=126°,∠AQF=100°,则∠A－∠F=()
Choices:
(A) 60°
(B) 46°
(C) 26°
(D) 45°
|
46°
| 29,697 | null |
46°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1228.jpg"
}
] |
<image>把一块直尺与一块含30°的直角三角板如图放置,若∠1=34°,则∠2的度数为()
Choices:
(A) 114°
(B) 124°
(C) 116°
(D) 126°
|
124°
| 29,707 | null |
124°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1239.jpg"
}
] |
<image>在△ABC中,AB=AC,∠A=50°,AB的垂直平分线DE交AC于D,垂足为E,则∠DBC的度数是()
Choices:
(A) 50°
(B) 40°
(C) 65°
(D) 15°
|
15°
| 29,718 | null |
15°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1271.jpg"
}
] |
<image>如图,已知AB=AC=AD,∠CBD=2∠BDC,∠BAC=42°,则∠CAD的度数为()度．
Choices:
(A) 56
(B) 78
(C) 84
(D) 112
|
84
| 29,750 | null |
84
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1274.jpg"
}
] |
<image>如图,已知a∥b,小明把三角板的直角顶点放在直线b上,若∠1=35°,则∠2的度数为()
Choices:
(A) 65°
(B) 120°
(C) 125°
(D) 145°
|
125°
| 29,753 | null |
125°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1284.jpg"
}
] |
<image>如图,已知,∠BAC=35°,⁀{CD}=80°,那么∠BOD的度数为()
Choices:
(A) 75°
(B) 80°
(C) 135°
(D) 150°
|
150°
| 29,763 | null |
150°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1310.jpg"
}
] |
<image>如图,直线AB⊥CD于O,直线EF交AB于O,∠COF=70°,则∠AOE等于()
Choices:
(A) 20°
(B) 30°
(C) 35°
(D) 70°
|
20°
| 29,789 | null |
20°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1317.jpg"
}
] |
<image>如图,⊙O的圆心角∠BOC=112°,点D在弦BA的延长线上且AD=AC,则∠D的度数为()
Choices:
(A) 28°
(B) 56°
(C) 30°
(D) 41°
|
28°
| 29,796 | null |
28°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1385.jpg"
}
] |
<image>如图,在△ABC中,∠C=90°,∠BDC=30°,AD=2BC,则∠A=()
Choices:
(A) 15°
(B) 20°
(C) 16°
(D) 18°
|
15°
| 29,864 | null |
15°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1406.jpg"
}
] |
<image>如图,将一块含有30°的直角三角板的顶点放在直尺的一边上,若∠1=48°,那么∠2的度数是()
Choices:
(A) 48°
(B) 78°
(C) 92°
(D) 102°
|
102°
| 29,885 | null |
102°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1418.jpg"
}
] |
<image>如图所示的是某超市入口的双买闸门,当它的双翼展开时,双翼边缘的端点A与B之间的距离为10cm,双翼的边缘AC=BD=54cm,且与闸机侧立面夹角∠PCA=∠BDQ=30°,求当双翼收起时,可以通过闸机的物体的最大宽度是()
Choices:
(A) 74cm
(B) 64cm
(C) 54cm
(D) 44cm
|
64cm
| 29,897 | null |
64cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1431.jpg"
}
] |
<image>如图,C是以AB为直径的半圆O上一点,连结AC,BC,分别以AC,BC为边向外作正方形ACDE,BCFG．DE,FG,⁀{AC},⁀{BC}的中点分别是M,N,P,Q．若MP+NQ=12,AC+BC=16,则AB的长为()
Choices:
(A) 9√{2}
(B) \frac{90}{7}
(C) 12
(D) 16
|
12
| 29,910 | null |
12
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1449.jpg"
}
] |
<image>如图,点A、B、C都在⊙O上,若∠BAO=40°,则∠C的度数为()
Choices:
(A) 40°
(B) 50°
(C) 80°
(D) 100°
|
50°
| 29,928 | null |
50°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1458.jpg"
}
] |
<image>如图,AB∥CD,AE平分∠CAB交CD于点E,若∠C=70°,则∠AED度数为()
Choices:
(A) 110°
(B) 125°
(C) 135°
(D) 140°
|
125°
| 29,937 | null |
125°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1478.jpg"
}
] |
<image>如图,一个底面圆周长为24m,高为5m的圆柱体,一只蚂蚁沿表面从点A到点B所经过的最短路线长为()
Choices:
(A) 12m
(B) 15m
(C) 13m
(D) 14m
|
13m
| 29,957 | null |
13m
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1552.jpg"
}
] |
<image>一个钢管放在V形架内,如图是其截面图,O为钢管的圆心．如果钢管的半径为25cm,∠MPN=60°,则OP=()
Choices:
(A) 50cm
(B) 25√{3}cm
(C) \frac{50√{3}}{3}cm
(D) 50√{3}cm
|
50cm
| 30,031 | null |
50cm
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1553.jpg"
}
] |
<image>如图,AB是⊙O的直径,若∠AOC=70°,且AD∥OC,则∠AOD的度数为()
Choices:
(A) 70°
(B) 60°
(C) 50°
(D) 40°
|
40°
| 30,032 | null |
40°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1557.jpg"
}
] |
<image>如图,PA、PB是⊙O的切线,A、B是切点,∠P=60°,PA=2,⊙O的直径等于()
Choices:
(A) \frac{2√{3}}{3}
(B) \frac{4√{3}}{3}
(C) 2
(D) 1
|
\frac{4√{3}}{3}
| 30,036 | null |
\frac{4√{3}}{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1575.jpg"
}
] |
<image>如图,已知⊙C的半径为2,圆外一点O满足OC=3.5,点P为⊙C上一动点,经过点O的直线l上有两点A、B,且OA=OB,∠APB=90°,l不经过点C,则AB的最小值为()
Choices:
(A) 2
(B) 2.5
(C) 3
(D) 3.5
|
3.5
| 30,054 | null |
3.5
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1579.jpg"
}
] |
<image>如图,AP为圆O的切线,P为切点,OA交圆O于点B,若∠A=40°,则∠APB等于()
Choices:
(A) 25°
(B) 20°
(C) 40°
(D) 35°
|
25°
| 30,058 | null |
25°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1666.jpg"
}
] |
<image>如图,点B,C,D在⊙O上,若∠BCD=120°,则∠BOD的度数是()
Choices:
(A) 60°
(B) 80°
(C) 120°
(D) 240°
|
120°
| 30,145 | null |
120°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1672.jpg"
}
] |
<image>如图,⊙O的直径AB长为10,弦BC长为6,OD⊥AC,垂足为点D,则OD长为()
Choices:
(A) 6
(B) 5
(C) 4
(D) 3
|
3
| 30,151 | null |
3
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1681.jpg"
}
] |
<image>如图,点A、B、C都是圆O上的点,在四边形ABCO中,∠AOC=140°,则∠B的度数为()
Choices:
(A) 110°
(B) 70°
(C) 140°
(D) 100°
|
110°
| 30,160 | null |
110°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1700.jpg"
}
] |
<image>如图,已知在⊙A中,B、C、D三个点在圆上,且满足∠CBD=2∠BDC．若∠BAC=44°,则∠CAD的度数为()
Choices:
(A) 68°
(B) 88°
(C) 90°
(D) 112°
|
88°
| 30,179 | null |
88°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1723.jpg"
}
] |
<image>如图,A、B、C、D四个点均在⊙O上,∠B=55°,AO∥DC,则∠AOD的度数为()
Choices:
(A) 70°
(B) 75°
(C) 80°
(D) 85°
|
70°
| 30,202 | null |
70°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1752.jpg"
}
] |
<image>如图,当圆形桥孔中的水面宽度AB为8米时,弧ACB恰为半圆．当水面上涨1米时,桥孔中的水面宽度A′B′为()
Choices:
(A) √{15}米
(B) 2√{15}米
(C) 2√{17}米
(D) 不能计算
|
2√{15}米
| 30,231 | null |
2√{15}米
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1756.jpg"
}
] |
<image>一张折叠型方桌子如图甲,其主视图如乙,已知AO=BO=50cm,CO=DO=30cm,现将桌子放平,要使桌面a距离地面m为40cm高,则两条桌腿需要叉开的角度∠AOB为()
Choices:
(A) 150°
(B) 约105°
(C) 120°
(D) 90°
|
120°
| 30,235 | null |
120°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1767.jpg"
}
] |
<image>如图,AB是⊙O的弦,AB=10,点C是⊙O上的一个动点,且∠C=45°．若点M、N分别是弦AB、AC的中点,则MN的最大值是()
Choices:
(A) 5√{2}
(B) 5
(C) √{5}
(D) 4
|
5√{2}
| 30,246 | null |
5√{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1777.jpg"
}
] |
<image>如图,在三角形ABC中,∠ACB=90°,∠B=50°,将此三角形绕点C沿顺时针方向旋转后得到三角形A′B′C,若点B′恰好落在线段AB上,AC、A′B′交于点O,则∠COA′的度数是()
Choices:
(A) 50°
(B) 60°
(C) 70°
(D) 80°
|
60°
| 30,256 | null |
60°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1791.jpg"
}
] |
<image>将一张宽度相等的长方形纸条按如图所示的方式折叠一下,如果∠1=140°,那么∠2的度数是()
Choices:
(A) 100°
(B) 110°
(C) 120°
(D) 140°
|
110°
| 30,270 | null |
110°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1803.jpg"
}
] |
<image>如图,用矩形ABCD纸片裁一扇形ABE,围成圆锥侧面．若AB=16,则此圆锥底面半径为()
Choices:
(A) 4
(B) 16
(C) 4√{5}
(D) 8
|
4
| 30,282 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1833.jpg"
}
] |
<image>我国纸伞的制作工艺十分巧妙．如图,伞不管是张开还是收拢,伞柄AP始终平分同一平面内两条伞骨所成的角∠BAC,且AE=AF,DE=DF,从而保证伞圈能沿着伞柄滑动．有一种玩具伞张开时,BDC在同一直线上,若AB=50cm,AD=14cm,则制作一把这样的纸伞需要油纸的面积是(不记接缝)()
Choices:
(A) 48cm^{2}
(B) 70πcm^{2}
(C) 2400πcm^{2}
(D) 2500πcm^{2}
|
2400πcm^{2}
| 30,312 | null |
2400πcm^{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1851.jpg"
}
] |
<image>如图,甲、乙两盏路灯相距30米,一天晚上,当小刚从路灯甲底部向路灯乙底部直行25米时,发现自己的身影顶部正好接触到路灯乙的底部,已知小刚的身高为1.5米,那么路灯甲的高为()
Choices:
(A) 9米
(B) 8米
(C) 7米
(D) 6米
|
9米
| 30,330 | null |
9米
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1964.jpg"
}
] |
<image>如图,两个直角三角形重叠在一起,将其中一个三角形沿着点B到点C的方向平移到△DEF的位置,∠B=90°,AB=8,DH=3,平移距离为4,求阴影部分的面积为()
Choices:
(A) 20
(B) 24
(C) 25
(D) 26
|
26
| 30,443 | null |
26
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/1967.jpg"
}
] |
<image>如图,一个高为1m的油筒内有油,一根木棒长1.2m,从桶盖小口斜插入桶内,一端到底部,另一端正好到小口,抽出木棒,量得棒上浸油部分的长0.36m,则桶内油的高度为()
Choices:
(A) 0.28m
(B) 0.385m
(C) 0.4m
(D) 0.3m
|
0.3m
| 30,446 | null |
0.3m
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2054.jpg"
}
] |
<image>如图,小明设计两个直角,来测量河宽BC,他量得AB=2米,BD=\frac{7}{3}米,CE=9米,则河宽BC为()
Choices:
(A) \frac{7}{2}米
(B) \frac{17}{2}米
(C) \frac{40}{7}米
(D) 11米
|
\frac{40}{7}米
| 30,533 | null |
\frac{40}{7}米
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2059.jpg"
}
] |
<image>现有一个测试距离为5m的视力表(如图),根据这个视力表,小华想制作一个测试距离为3m的视力表,则图中的的值为()
Choices:
(A) \frac{3}{2}
(B) \frac{2}{3}
(C) \frac{3}{5}
(D) \frac{5}{3}
|
\frac{5}{3}
| 30,538 | null |
\frac{5}{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2103.jpg"
}
] |
<image>如图,点O为优弧ACB所在圆的圆心,∠AOC=104°,点D在AB的延长线上,BD=BC,则∠D的度数为()
Choices:
(A) 26°
(B) 27°
(C) 30°
(D) 52°
|
26°
| 30,582 | null |
26°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2160.jpg"
}
] |
<image>如图,△ABC内接于⊙O,AD为⊙O的直径,交BC于点E,若DE=2,OE=3,则tanC•tanB=()
Choices:
(A) 2
(B) 3
(C) 4
(D) 5
|
4
| 30,639 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2167.jpg"
}
] |
<image>如图,边长为1的小正方形构成的网格中,⊙O半径为1,圆心O在格点上,则tan∠AED=()
Choices:
(A) 1
(B) \frac{√{2}}{2}
(C) \frac{1}{2}
(D) \frac{√{3}}{3}
|
\frac{1}{2}
| 30,646 | null |
\frac{1}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2209.jpg"
}
] |
<image>如图,⊙O中,若∠BOD=140°,∠CDA=30°,则∠AEC的度数是()
Choices:
(A) 80°
(B) 100°
(C) 110°
(D) 125°
|
100°
| 30,688 | null |
100°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2210.jpg"
}
] |
<image>在Rt△ABC中∠C=90°,AB=6,sinA=\frac{2}{3},则AC的长为()
Choices:
(A) 4
(B) 2√{5}
(C) \frac{18√{13}}{13}
(D) \frac{13√{13}}{12}
|
2√{5}
| 30,689 | null |
2√{5}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2220.jpg"
}
] |
<image>如图,已知CD是⊙O的直径,过点D的弦DE平行于半径OA,若∠D的度数是50°,则∠C的度数是()
Choices:
(A) 25°
(B) 30°
(C) 40°
(D) 50°
|
25°
| 30,699 | null |
25°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2316.jpg"
}
] |
<image>如图,△ABC是⊙O的内接三角形,AB=AC,∠BCA=65°,作CD∥AB,并与⊙O相交于点D,连接BD,则∠DBC的大小为()
Choices:
(A) 15°
(B) 35°
(C) 25°
(D) 45°
|
15°
| 30,795 | null |
15°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2319.jpg"
}
] |
<image>如图所示,在Rt△BAD中,延长斜边BD到点C,使DC=\frac{1}{2}BD,连接AC,若tanB=\frac{5}{3},则tan∠CAD的值为()
Choices:
(A) \frac{√{3}}{3}
(B) \frac{√{3}}{5}
(C) \frac{1}{3}
(D) \frac{1}{5}
|
\frac{1}{5}
| 30,798 | null |
\frac{1}{5}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2350.jpg"
}
] |
<image>如图,⊙O的半径为5,AB为弦,点C为⁀{AB}的中点,若∠ABC=30°,则弦AB的长为()
Choices:
(A) \frac{1}{2}
(B) 5
(C) \frac{5√{3}}{2}
(D) 5√{3}
|
5√{3}
| 30,829 | null |
5√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2357.jpg"
}
] |
<image>如图,AB为⊙O的直径,点C,D在⊙O上．若∠AOD=30°,则∠BCD等于()
Choices:
(A) 75°
(B) 95°
(C) 100°
(D) 105°
|
105°
| 30,836 | null |
105°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2367.jpg"
}
] |
<image>如图,AB是⊙O的直径,C,D为⊙O上的两点,若AB=6,BC=3,则∠BDC的大小是()
Choices:
(A) 60°
(B) 45°
(C) 30°
(D) 15°
|
30°
| 30,846 | null |
30°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2401.jpg"
}
] |
<image>把Rt△ABC与Rt△CDE放在同一水平桌面上,摆放成如图所示的形状,使两个直角顶点重合,两条斜边平行,若∠B=25°,∠D=58°,则∠BCE的度数是()
Choices:
(A) 83°
(B) 57°
(C) 54°
(D) 33°
|
57°
| 30,880 | null |
57°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2408.jpg"
}
] |
<image>如图,已知BC是⊙O的直径,过点B的弦BD平行于半径OA,若∠B的度数是50°,则∠C的度数是()
Choices:
(A) 50°
(B) 40°
(C) 30°
(D) 25°
|
25°
| 30,887 | null |
25°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2420.jpg"
}
] |
<image>如图,∠BAD=90°,∠ADC=30°,∠BCD=142°,则∠B=()
Choices:
(A) 12°
(B) 20°
(C) 22°
(D) 42°
|
22°
| 30,899 | null |
22°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2428.jpg"
}
] |
<image>如图,半径为4的⊙O中,已知弦AB=1,∠BCA+∠EAD=90°,则弦DE的长为()
Choices:
(A) 5
(B) √{65}
(C) 7
(D) 3√{7}
|
3√{7}
| 30,907 | null |
3√{7}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2432.jpg"
}
] |
<image>如图,已知O是四边形ABCD内一点,OA=OB=OC,∠ABC=∠ADC=65°,则∠DAO+∠DCO=()
Choices:
(A) 90°
(B) 110°
(C) 120°
(D) 165°
|
165°
| 30,911 | null |
165°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2452.jpg"
}
] |
<image>如图,已知AB=AC=AD,∠CBD=44°,则∠CAD的度数为()
Choices:
(A) 68°
(B) 88°
(C) 90°
(D) 112°
|
88°
| 30,931 | null |
88°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2507.jpg"
}
] |
<image>如图,⁀{BC}=⁀{CD}=⁀{DE},已知AB是⊙O的直径,∠BOC=40°,那么∠AOE=()
Choices:
(A) 40°
(B) 60°
(C) 80°
(D) 120°
|
60°
| 30,986 | null |
60°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2590.jpg"
}
] |
<image>如图,是一个圆形展厅,为了监控整个展厅,在其圆形边缘上安装了甲、乙两台监视器,若甲监视器的监控角度为65°,则乙监控器的监控角度至少为()
Choices:
(A) 25°
(B) 65°
(C) 115°
(D) 130°
|
115°
| 31,069 | null |
115°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2616.jpg"
}
] |
<image>如图,AB是⊙O的直径,∠ADC=30°,OA=2,则AC的长为()
Choices:
(A) 2
(B) 4
(C) 2√{3}
(D) √{3}
|
2√{3}
| 31,095 | null |
2√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2618.jpg"
}
] |
<image>如图,BC是⊙O的直径,若⁀{AC}度数是50°,则∠ACB的度数是()
Choices:
(A) 25°
(B) 40°
(C) 65°
(D) 130°
|
65°
| 31,097 | null |
65°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2624.jpg"
}
] |
<image>如图,一个量角器的底端A、B分别在y轴正半轴与x轴负半轴上滑动,点D位于该量角器上128°刻度处．当点D与原点O的距离最大时,∠OAB=()
Choices:
(A) 64°
(B) 52°
(C) 38°
(D) 26°
|
26°
| 31,103 | null |
26°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2636.jpg"
}
] |
<image>如图,四边形ABCD内接于圆O,E为CD延长线上一点,若∠B=110°,则∠ADE的度数为()
Choices:
(A) 115°
(B) 110°
(C) 90°
(D) 80°
|
110°
| 31,115 | null |
110°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2655.jpg"
}
] |
<image>如图,四边形ABCD内接于⊙O,F是上一点,且=,连接CF并延长交AD的延长线于点E,连接AC．若∠ABC=110°,∠BAC=20°,则∠E的度数为()
Choices:
(A) 60°
(B) 55°
(C) 50°
(D) 45°
|
50°
| 31,134 | null |
50°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2660.jpg"
}
] |
<image>如图,四边形ABCD内接于⊙O,F是⁀{CD}上一点,且⁀{DF}=⁀{BC},连接CF并延长交AD的延长线于点E,连接AC．若∠ABC=110°,∠BAC=25°,则∠E的度数为()
Choices:
(A) 45°
(B) 50°
(C) 55°
(D) 60°
|
45°
| 31,139 | null |
45°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2740.jpg"
}
] |
<image>如图,两圆相交于A,B两点,小圆经过大圆的圆心O,点C,D分别在两圆上,若∠ADB=100°,则∠ACB的度数为()
Choices:
(A) 35°
(B) 40°
(C) 50°
(D) 80°
|
40°
| 31,219 | null |
40°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2753.jpg"
}
] |
<image>如图所示,AB=AC,AD=AE,∠BAC=∠DAE,∠1=25°,∠2=30°,则∠3=()
Choices:
(A) 60°
(B) 55°
(C) 50°
(D) 无法计算
|
55°
| 31,232 | null |
55°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2770.jpg"
}
] |
<image>如图,AB为⊙O的直径,点C、D在⊙O上,若∠AOD=30°,则∠BCD的度数是()
Choices:
(A) 150°
(B) 120°
(C) 105°
(D) 75°
|
105°
| 31,249 | null |
105°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2775.jpg"
}
] |
<image>如图,△ABC是⊙O的内接三角形,D是AB边的中点,OA=6,∠ACB=30°,则OD=()
Choices:
(A) 6
(B) 3√{3}
(C) 3
(D) \frac{3√{3}}{2}
|
3√{3}
| 31,254 | null |
3√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2784.jpg"
}
] |
<image>如图,△ABC是⊙O的内接三角形,∠C=30°,⊙O的半径为5,若点P是⊙O上的一点,在△ABP中,PB=AB,则PA的长为()
Choices:
(A) 5
(B) \frac{5√{3}}{2}
(C) 5√{2}
(D) 5√{3}
|
5√{3}
| 31,263 | null |
5√{3}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2792.jpg"
}
] |
<image>如图,△ABC内接于⊙O,AH⊥BC于点H,若AC=8,AH=6,⊙O的半径OC=5,则AB的值为()
Choices:
(A) 5
(B) \frac{13}{2}
(C) 7
(D) \frac{15}{2}
|
\frac{15}{2}
| 31,271 | null |
\frac{15}{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/2817.jpg"
}
] |
<image>如图,AB是⊙O的弦,作OC⊥OA交⊙O的切线BC于点C,交AB于点D．已知∠OAB=20°,则∠OCB的度数为()
Choices:
(A) 20°
(B) 30°
(C) 40°
(D) 50°
|
40°
| 31,296 | null |
40°
|
[
{
"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/2940.jpg"
}
] |
<image>如图,PA、PB、AB都与⊙O相切,∠P=40°,则∠AOB等于()
Choices:
(A) 40°
(B) 50°
(C) 60°
(D) 70°
|
70°
| 31,419 | null |
70°
|
[
{
"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/2961.jpg"
}
] |
<image>如图,过⊙O外一点P引⊙O的两条切线PA、PB,切点分别是A、B,OP交⊙O于点C,点D是优弧AB上不与点A、点B重合的一个动点,连接AD、CD,若∠APB=76°,则△ADC的度数为()
Choices:
(A) 26°
(B) 20°
(C) 16°
(D) 30°
|
26°
| 31,440 | null |
26°
|
[
{
"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/3011.jpg"
}
] |
<image>如图,过⊙O外一点P引⊙O的两条切线PA、PB,切点分别是A、B,OP交⊙O于点C,点D是⁀{ABC}上不与点A、点C重合的一个动点,连接AD、CD,若∠APB=80°,则∠ADC的度数是()
Choices:
(A) 15°
(B) 20°
(C) 25°
(D) 30°
|
25°
| 31,490 | null |
25°
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3014.jpg"
}
] |
<image>如图1,⊙O的直径AB=2,⊙O的切线CD与AB的延长线交于点C,D为切点,∠C=30°,则AD等于()
Choices:
(A) √{3}
(B) 2
(C) 1
(D) \frac{√{3}}{2}
|
√{3}
| 31,493 | null |
√{3}
|
[
{
"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/3061.jpg"
}
] |
<image>如图,点C是半圆O的直径AB的延长线上一点．CD与半圆O相切,D为切点,过点D作DE∥AB交半圆O于点E．若四边形OCDE是平行四边形,CD=4,则ED的长为()
Choices:
(A) 4
(B) 4√{2}
(C) 2√{6}
(D) 3√{3}
|
4√{2}
| 31,540 | null |
4√{2}
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3094.jpg"
}
] |
<image>如图,在Rt△AOB中,OA=OB=5,⊙O的半径为3,点P是AB边上的动点,过点P作⊙O的一条切线PQ(点Q为切点),则切线PQ的最小值为()
Choices:
(A) 3
(B) 5√{2}-3
(C) 4
(D) 5
|
4
| 31,573 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3165.jpg"
}
] |
<image>如图,一块四边形绿化园地,四角都做有半径为2的圆形喷水池,则这四个喷水池占去的绿化园地的面积为()
Choices:
(A) 4π
(B) 8π
(C) 16π
(D) 不能确定
|
4π
| 31,644 | null |
4π
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3185.jpg"
}
] |
<image>如图,已知a∥b∥c,AB=1,BC=2,EF=4,则DE=()
Choices:
(A) 1
(B) 2
(C) 3
(D) 4
|
4
| 31,664 | null |
4
|
[
{
"bytes": null,
"path": "/blob/v-xiyaowang/v-xiyaowang/llava_prm/llava_prm/images/GeoQA/3198.jpg"
}
] |
<image>如图,在△ADE中,BC∥DE,AB=3,BD=DE=6,则BC的长是()
Choices:
(A) 2
(B) 3
(C) 4
(D) 6
|
4
| 31,677 | null |
4
|
[
{
"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/3227.jpg"
}
] |
<image>如图,△ABC中,点D、E分别在边AB、BC上,DE∥AC,若DB=4,AB=6,BE=3,则EC的长是()
Choices:
(A) 4
(B) 2
(C) \frac{3}{2}
(D) \frac{5}{2}
|
\frac{3}{2}
| 31,706 | null |
\frac{3}{2}
|
[
{
"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}
|
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