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好题月月练

好题月月练
好题月月练

好题月月练

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一.选择题

1.如图,AB是⊙O的直径,点C在⊙O上,则∠ACB的度数是()。

A.30 °

B.45°

C.60°

D.90°

2.如图,已知圆心角∠BOC=78°,则圆周角∠BAC的度数是()。

A.156°

B.78°

C.39°

D.12°

3.如图所示,圆O的弦AB垂直平分OC,则四边形OABC是()。

A.正方形

B.长方形

C.菱形

D.以上答案都正确

4.如图,AB是⊙O的弦,OC⊥AB于点C,若AB=8㎝,OC=3㎝,则⊙O的半径为㎝。

5.如图,半圆的直径AB= 。

6.如图,⊙O中弧AB的度数为60°,AC是⊙O的直径,那么∠BOC等于()。

A.150°

B.130°

C.120°

D.60°

第6题图第10题图第12题图

7.下列命题是真命题的是()。

A.垂直于圆的半径的直线是圆的切线。

B.经过半径外端的直线是圆的切线。

C.直线上一点到圆心的距离等于圆的半径的直线是圆的切线。

D.到圆心的距离等于圆的半径的直线是圆的切线。

8. ⊙O的半径R,圆心到点A的距离为d,且R、d分别是方程x2—6x+8=0的两根,

则点A与⊙O的位置关系是()。

A. 点A在⊙O内

B.点A在⊙O上

C.点A在⊙O外

D. 点A不在⊙O上

9.下列5个命题:

(1)两个端点能完全重合的弧是等弧。(2)圆的任意一条弧必定把圆分成优弧和劣弧两部分。(3)经过平面上任意三点可作一个圆。(4)任意一个圆有且只有一个内接三角形。(5)三角形的外心到各顶点距离相等。其中真命题有( ).

A.1个

B.2个

C.3个

D.4个

10.如图,⊙O外接于△ABC,AD为⊙O的直径,∠ABC=30°,则∠CAD=()。

A.30°

B.40°

C.50°

D.60°

11.O是△ABC的外心,且∠ABC+∠ACB=100°,则∠BOC=()。

A.100°

B. 120°

C.130°

D.160°

12.如图,△ABC的三边分别切⊙O于D、E、F,若∠A=50°,则∠DEF=()。

A.65°

B. 50°

C.130°

D.80°

13.在Rt△ABC中,∠C=90°,AB=5,内切圆半径为1,则三角形周长为()。

A.15

B.12

C.13

D.14

14.已知,两圆的圆心距为3,两圆的半径分别是方程x2-4x+3=0的两根,那么这两个圆的位置关系是()。A. 外离 B.外切 C.相交 D.内切

15. ⊙O的半径为3㎝,点M是⊙O外一点,OM=4㎝,则以点M为圆心且与⊙O相切的圆的半径一定是()。A.1㎝或7㎝ B.1㎝ C.7㎝ D. 不确定

二.填空题

16.如图,在⊙O中,AB为直径,∠ACB的平分线交⊙O于D,则∠ABD=。

第16题图第19题图第20题图

17.已知⊙O的半径为2,点P 为⊙O外一点,OP长为3,那么以P为圆心且与⊙O相切的圆的半径为。

18.在Rt△ABC中,∠C=90°,AC=5,BC=12,以C为圆心,R为半径作圆与斜边AB相切,则R的值为。

19.如图所示,△ABC内接⊙O,AB=AC,∠BOC=100°,MN是过B点而垂直OB的直线,则∠ABM= ,∠CBN= 。

20.如图所示,,有一圆形展厅,在其圆形边缘上的A点处安装了一台监听器,他的监控角度是65°,为了监控整个展厅,最少需在圆形边缘上共装这样的台。

21.小刚对科技馆富有创意的科学方舟形象设计很有兴趣,他回家后将一政五边形纸片沿其对称轴对折,旋转齐放,做成科学方舟模型。如图所示,改正五边形

的边心距OB长为,AC为科学方舟A到船头的距离,请计算。

三,解答题

22.已知,如图,在△ABC中,AB=AC,以AB为直径的⊙O交BC于点D,作DE⊥AC于点E。

求证:DE为⊙O的切线。

23.如图,ABCD是⊙O的内接四边形,DP∥AC,交BA的延长线于P。

求证:AD×DC=PA×BC

24.如图,AD为△ABC外接圆的直径,AD⊥BC,垂足为点F,∠ABC的平分线交AD于点E,连接BD,CD.

(1)求证:BD=CD;

(2)小明说:“B,E,C三点在以D为圆心,以DB为半径的圆上。”你认为小明的说法正确吗?请说明理由。

25.机器人“海宝”在某圆形区域表演“按指令行走”,如图所示,“海宝”从圆心O出发,先沿北偏西60°方向行走8米至点A处,再沿正南方向行走10米至B处,最后沿正东方向行走至点C处,点B,C都在圆O上。

(1)求圆O的半径。

(2)求弦BC的长。

26.设直线l到⊙O的圆心的距离为d,半径为R,并使,试由关于x的一元二次方程根的情况讨论l与⊙O的位置关系

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