2013中考圆的有关性质试题汇编.(2)doc

B A

E E D O C

B A 2013中考圆的有关性质试题汇编（2）

A 组

一选择题

1. 如图，AB 是半圆的直径，点C 是弧AB 的中点，点E 是弧AC 的中点，

连结EB 、CA 交于点F ，则BF EF

为( )

A. 13

B. 14

12-

D. 21

2．如图，AB 是⊙O 的直径，点D 在AB 的延长线上，DC 切⊙O 于C ，若25A =

∠．则D ∠等于（） A ．

20 B

．

30 C ．

40 D ．

4.如图，⊙O 的半径OA=5，以A 为圆心，OA 为半径的弧交⊙O 于B 、C 两点，则BC 等于( ).

A.35

B. 25

C. 3

D. 8

5．如图，△ABC 内接于⊙O ，其外角平分线AD 交⊙O 于DM ⊥AC 于M ，下列结论： ①DB=DC ；②AC-AB=2AM ；③AC+AB=2CM ；④

ABD ?=2

CD B

?其中正确的有( )

A ．只有④②

B ．只有①②③

C ．只有③④

D ．①②③④

6. 如图，AB 是⊙O 的直径，CD 为弦，AB CD ⊥于E ，则下列结论中不成立的是Ａ．∠A ﹦∠D Ｂ．CE ﹦DE Ｃ．∠ACB ﹦90° D ．CE ﹦BD

7．如图，已知AB 、CD 是⊙O 的两条直径, 且∠AOC=50°，过A 作AE ∥CD 交⊙O 于E ，则∠AOE 的度数为 ( ) A ．65° B.70° C.75° D.80° 8．如图，AB 是⊙O 的直径，弦CD ⊥AB 于点E ，∠CDB ＝30°，⊙O 的半径为3cm ，则圆心O 到弦CD 的距离为( ) A ．3

2 cm

B ．

3 cm

C ．3 3 cm

D ．6cm

O A C B D E 第7题图

O B C

D A

（第13图）

9．如图，A ，B ，C ，D 为⊙O 的四等分点，动点P 从圆心O 出发，沿O —C —D —O 路线作匀速运动，设运动时间为x(秒)，∠APB ＝y(度)，右图函数图象表示y 与x 之间函数关系，则点M 的横坐标应为（）

A ．2

B ．2π

C ．1

2π+ D ．2π

＋2

11、如图，⊙P 内含于⊙O ，⊙O 的弦AB 切⊙P 于点C ，且OP AB //．若阴影部分的面积为π9，则弦AB 的长为（） A ．3

B ．4

C ．6

D ．9

12、如图，已知⊙O 的半径为10，弦12,AB =M 是AB 上任意一点，则线段OM 的长可能是（）A ．5

B ．7

C ．9

D ．11

13.如图，BD 是⊙O 的直径，CBD ∠=30 ，则∠A 的度数为（）A ．30

B ．45

C ．60

D ．75

14.如6题图，△ABC 是⊙O 的内接三角形，若∠ABC ＝70°，则∠AOC 的度数等于（） A ．140° B ．130° C ．120° D ．110° 15．如图，已知⊙O 的弦AB 、CD 相交于点E ，

的度数为60°，

的度数为100°，则∠AEC 等于（）

A. 60°

B. 100°

C. 80°

D. 130° 二填空题

1．如图，将半径为2cm 的圆形纸片折叠后，圆弧恰好经过圆心O ，则折痕AB 的长为 cm ．

2. 如图，两正方形彼此相邻且内接于半圆，若小正方形的面积为1cm2，则该半圆的直径为__________。

3.如图，AB 是⊙O 的直径，点D 在⊙O 上，∠AOD ＝130°，BC ∥OD 交⊙O 于C ，则∠A ＝ °． (第4题) （第5题） O

B D A （第11题）

C P

O 15题图

90 1 M x

y 45

（第9题）

O A B M 第12题

4．如图，⊙O 是△ABC 的外接圆，∠OBC ＝20°，则∠A= °．

5．如图，四边形ABCD 是⊙O 的内接正方形，点P 是劣弧CD 上不同于点C 的任意一点，

则∠BPC 的度数是． 6．如图，AB 是⊙O 直径，且AB=4cm ，弦CD ⊥AB ，∠COB=45°，则CD 为 cm ．

7．如图，点C′与半圆上的点C 关于直径AB 成轴对称．若∠AOC ＝40°，则∠CC′B ＝ °． 8.如图，△ABC 内接于⊙O ，AC 是⊙O 的直径，∠ACB=40°，点D 是弧BAC 上一点，则∠D 的度数是______． 9、如图，CD 是⊙O 的直径，弦AB ⊥CD 于点H ，若∠D=30°，CH=1cm ，则AB= cm ．

10、在半径为5的⊙O 中，有两平行弦AB ．CD ，且AB ＝6，CD ＝8，则弦AC 的长为__________．

11. 已知⊙O 的半径为26cm ，弦AB//CD ，AB=48cm ，CD=20cm ，则AB 、CD 之间的距离为 12、已知一个半圆形工件，未搬动前如图所示，直径平行于地面放置，搬动时为了保护圆弧部分不受损伤，先将半圆作如图所示的无滑动翻转，使它

的直径紧贴地面，再将它沿地面平移50米，半圆的直径为4米，则圆心O 所经过的路线长是_________．

三解答题 1．（8分）如图，AB 是⊙O 的直径，BC 是⊙O 的切线，D 是⊙O 上的一点，且AD ∥OC ，OC 与BD 交于E ，若AO ＝2，BC ＝23，求：（1）求∠A 的度数；（2）求DE 的长

A C D O

B A B

C ′

O C 40 O A

B C D A B O

O O l

2．如图，已知AB 是⊙O 的直径，直线CD 与⊙O 相切于点C ，过A 作AD ⊥CD ，D 为垂足。（1）求证：AC 平分∠DAB 。（2）若AD=3，AC=15，求AB 的长。

3.如图，AB 为⊙O 的直径，弦CD ⊥AB ，垂足为点M ，AE 切⊙O 于点A ，交BC 的延长线于点E ，连接AC. (1)若B=30°，AB=2，求CD 的长；(2)求证：AE 2

=EB ·EC.

4、如图，点O 是△ABC 的内切圆的圆心，∠BAC=80°，求∠BOC 的度数。

6、如图，AB 是⊙O 的直径，且AB=4，AC 是弦，∠CAB=40°，求劣弧

BC 和弦AC 的长. （弧长计算结果保留，弦长精确到0.01）

第6题

B A E D O

C B A O

D C B

A B 组

.圆的有关性质

一选择题

1. 如第8题图，在△ABC 中，AB ＝AC ＝5,BC ＝8。⊙O 经过B 、C 两点，且AO=4,则⊙O 的半径长是（） A. 417或 B. 465或 C.

1765或 D. 41765或或

2.如图，已知，AB 是⊙O 的直径，点C ，D 在⊙O 上，∠ABC=50°，则∠D 为 A ．50° B ．45°

C ．40°

D ． 30°

3．如图，AB 为圆O 的直径，弦CD ⊥AB ，垂足为点E ，联结OC ，若OC=5，AE=2，则CD 等于 A ．3 B ．4 C ．6 D ．8

4．如图，△ABC 内接于⊙O ，AD 是⊙O 的直径，∠ABC ＝25°，则∠CAD 的度数是（） A ．25° B ．60° C ．65° D ．75°

5.如图，AB 是⊙O 的直径，BC 、CD 、DA 是⊙O 的弦，且BC=CD=DA ，则∠BCD=( ) A.1050 B.1200 C.1350 D.1500

6．如图，点A 在半径为3的⊙O 内，OA=3，P 为⊙O 上一点，当∠OPA 取最大值时，PA 的长等于（）.

A ．3

2 B ．6 C ．32 D ．23

7.如图， AB 是⊙O 的直径，CD 为弦，AB CD ⊥于E ，则下列结论中不成立的是（）.

Ａ．∠A ﹦∠D Ｂ．CE ﹦DE Ｃ．∠AC B ﹦90° D ．CE ﹦BD

8.已知⊙O 的半径为3cm ，点P 到圆心O 的距离为cm 5．则点P 与⊙O 的位置关系是（）. A ．点P 在⊙O 内 B ．点P 在⊙O 上

C ．点P 在⊙O 外

D ．不能确定

O E D

（3题图）

（第4题）第6题图

B C

· 第5题图图5

B A

D C B

（1题图）

二填空题

1．如图，AB 为⊙O 的弦，⊙O 的半径为5，OC ⊥AB 于点D ，交⊙O 于点C ，且CD ＝l ，则弦AB 的长是．

2.如图5，⊙Ｏ上的三点Ａ、Ｂ、Ｃ，若∠ＡＯＢ＝５６°，则∠ＡＣＢ等于 °

3.如图，⊙O 是△ABC 的外接圆，OD ⊥AB 于点D 、交⊙O 于点E ， ∠C=60°，如果⊙O 的半径为2，那么OD=

4.已知：如图，AB ，BC 为⊙O 的弦，点D 在AB 上，若4=OD ，10=BC ，

?=∠=∠60B ODB ，则DB 的长为

5.已知半径为5cm 的圆O 上弦长AB=8cm,则O 到弦AB 的距离为

三解答题

1．已知：如图，在△ABC 中，AB=AC ，以AB 为直径的⊙O 分别交BC 、AC 于点D 、E ，联结EB 交OD 于点F ．（1）求证：OD ⊥BE ；（2）若DE=5，AB=5，求AE 的长．

2.如图9，ＡＢ为⊙Ｏ的直径，弦ＣＤ⊥ＡＢ于点Ｅ．（１）当ＡＢ＝１０，ＣＤ＝６时，求ＯＥ的长；

（２）∠ＯＣＤ的平分线交⊙Ｏ于点Ｐ，当点Ｃ在上半圆（不包括Ａ、Ｂ点）上移动时，对于点Ｐ，下面三个结论：

①到ＣＤ的距离保持不变；②平分下半圆；③等分

DB ．其中正确的为（）

请予以证明．

3.有一座圆弧形的拱桥，桥下水面宽度8 m ，拱顶高出水面2 m 。现有一货船载一货箱

欲从桥下经过，已知货箱宽6m ，高1.5m(货箱底与水面持平)，问该货船能否顺利通过该桥？

4 . 如图，△ABC 内接于⊙O ，AD 是的边BC 上的高，AE 是⊙O 的直径，连BE ． ⑴求证：△ABE 与△ADC 相似；

⑵若AB=2BE=4DC=8，求△ADC 的面积.

D C

A O

图9 D

A O B

A B

O D C

D C

F E A B A B E

O D C

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