2021年中考必备：选填压轴分类汇编--圆的解题技巧及真题演练

2021年中考必备-圆选填压轴分类汇编

A 类：面积问题

技巧：多连半径，探讨线段，角度关系，以角导边

1．（2017·湖北省中考模拟）如图，在Rt △AOB 中，∠AOB=90°，OA=2，OB=1，将Rt △AOB 绕点O 顺时针旋转90°后得Rt △FOE ，将线段EF 绕点E 逆时针旋转90°后得线段ED ，分别以O ，E 为圆心，OA 、 ED 长为半径画弧AF 和弧DF ，连接AD ，则图中阴影部分面积是（） A ．π

B ．5π+

C ．

144

- D ．

104

- 2．（2020·河北省初三期末）如图，以等边ABC ?的一边AB 为直径的半圆O 交AC 于点D ，交BC 于点E ，若

4AB =，则阴影部分的面积是（）

．B

．C

D ．2

3．（2021·浙江省初三二模）如图，已知矩形ABCD 的周长为16，E 和F 分别为ABC ?和ADC ?的内切圆，

连接AE ，CE ，AF ，CF ，EF ，若

AECF ABCD

S S =

四边形矩形，则EF 的长为（） A

．B

．C

．

．4．（2020·柘城县实验中学初三二模）如图，点O 为Rt ABC 的斜边AB 的中点，90C ∠=?，30A ∠=?，以点O 为旋转中心顺时针旋转ABC 得到111A B C △，若2BC =，当11BC AC ∥时，图中弧1BC 所构成的阴影部分面积为（）． A

．

5．（2020·湖北省初三二模）如图，在Rt ABC 中，90C ∠=?，6AB =，AD 是BAC ∠的平分线，经过A ，D 两点的圆的圆心O 恰好落在AB 上，O 分别与AB 、AC 相交于点E 、F ．若圆半径为2．则阴影部分面积（）． A ．1

B ．43

C ．

π D

3- 6．（2020·山西省初三月考）如图，在Rt ABC

中，90,30,ACB A BC ∠=?∠=?=以直角边AC 为直径作O

交AB 于点D ，则图中阴影部分的面积是（） A

．3π

．6π-

．6π

7．（2020·山东大学附属中学初三月考）如图，将矩形ABCD 绕点A 逆时针旋转90°至矩形AEFG ，点D 的旋转路径为DG ，若AB ＝2，BC ＝4，则阴影部分的面积为（）

A ．

B ．

π C ．

+D ．

+8．（2020·合肥一六八中学初三一模）如图，以AD 为直径的半圆O 经过Rt △ABC 斜边AB 的两个端点，交直角边AC 于点E ，B 、E 是半圆弧的三等分点，弧BE 的长为

π，则图中阴影部分的面积为（）

A ．

π B C 32π- D 23

π-

9．（2020·山西省初三零模）如图，在

O 的内接正方形ABCD 中，AB =，以点A 为圆心，AD 长为半径车

弧，得到BD ，则图中阴影部分的面积为（） A ．1

B ．

- C ．1π-

D ．22

10．（2020·泰安市黄前中学初三一模）如图，菱形ABCD 的边长为2，∠A=60°，以点B 为圆心的圆与AD 、DC 相切，与AB 、CB 的延长线分别相交于点E 、F ，则图中阴影部分的面积为（）

A 2

B π

C 2

D ．2

11．（2020·内蒙古自治区初三三模）如图，90AOB ∠=?，30B ∠=?，以点O 为圆心，OA 为半径作弧交AB 于点A ，点C ，交OB 于点D ，若3OA =，则阴影部分的面积为_____.

12．（2020·山东省初三一模）如图，在扇形AOB 中，120AOB ?∠=，半径OC 交弦AB 于点D ，且OC OA ⊥．若

=OA _____．

13．（2020·浙江省初三一模）如图，在△ABC 中，∠ACB ＝90°，D 是BC 边上的点，CD ＝2，以CD 为直径的⊙与AB 相切于点E ．若弧DE 的长为

π，则阴影部分的面积_____．（保留π） 14．（2020·东莞市横沥中学初三二模）如图，四边形ABCD 是菱形，∠A ＝60°，AB ＝2，扇形EBF 的半径为2，圆心角为60°，则图中阴影部分的面积是_____．

15．（2020·广东华侨中学初三其他）如图，如图，在菱形ABCD 中，2AB =，60DAB ∠=?，把菱形ABCD 绕点A 顺时针旋转30°

得到菱形AB C D '''，其中点C 的运动路径为CC ，则图中阴影部分的面积为_________． 16．（2020·山东省初三二模）如图，在菱形ABCD 中，对角线AC ，BD 交于点O ，∠ABC =60°，AB =2，分别以点A 、点C 为圆心，以AO 的长为半径画弧分别与菱形的边相交，则图中阴影部分的面积为______．（结果保留π） 17．（2020·郑州市第八中学初三其他）如图所示，在Rt △ABC 中，90ACB ∠=?，30BAC ∠=?，2BC =，将三角形绕着BC 的中点O 逆时针旋转60?，点A 的对应点为E ，则图中阴影部分的面积为______． 18．（2019·河南省河南师大附中初三其他）如图，ABC 的内切圆

O 与BC,CA,AB 分别相切于点,,D E F ，且

5,13AB BC ==，12CA =，则阴影部分的面积为_______ (结果保留π)．

19．（2020·浙江省初三其他）如图，在菱形ABCD 中，160AB DAB =∠=?，，把菱形ABCD 绕点A 顺时针旋转30°得到菱形AB C D '''，其中点C 的运动路径为'CC ，则图中阴影部分的面积为________．

20．（2020·广西壮族自治区初三学业考试）如图，矩形ABCD 中，4BC =，2CD =，以AD 为直径的半圆O 与BC 相切于点E ，连接BD ，则阴影部分的面积为__．（结果保留)π

B 类：最值问题

技巧：善于添辅助线围三角形，三边关系求解。必要时添加辅助圆

21．（2020·合肥市第四十八中学初三一模）如图，等腰Rt ABC ?的一个锐角顶点A 是

O 上的一个动点，

90ACB ∠=?，腰AC 与斜边AB 分别交O 于点,E D ，分别过点,D E 作O 的切线交于点F ，且点F 恰好是

腰BC 上的点，连接,,OC OD OE ，若O 的半径为4，则OC 的最大值为：（）

A ．2

B ．2

C ．6

D ．8

22．（2020·山东省初三二模）如图，在平面直角坐标系中，已知点A （0，1）、点B （0，1+t ）、C （0，1﹣t ）（t ＞0），点P 在以D （3，5）为圆心，1为半径的圆上运动，且始终满足∠BPC=90°，则t 的最小值是（） A ．3

B ．4

C ．5

D ．6

23．（2020·广东省初三其他）如图，AB 是半圆O 的直径，4AB =，点C ，D 在半圆上，OC AB ⊥，2BD CD =，

点P 是OC 上的一个动点，则BP DP +的最小值为（）

A ．

B ．

C ．2

D ．24．（2020·山东省初三二模）如图，矩形ABCD 中，AB ＝2，AD ＝3，点

E 、

F 分别为AD 、DC 边上的点，且EF ＝2，点

G 为EF 的中点，点P 为BC 上一动点，则P A +PG 的最小值为（）

A ．3

B ．4

C ．

D ．5

25．（2020·山东省初三一模）如图，P 为⊙O 内的一个定点，A 为⊙O 上的一个动点，射线AP 、AO 分别与⊙O 交于

B 、

C 两点．若⊙O 的半径长为3，OP BC 的最大值为（）

A ．

B ．3

D ．

26．（2020·北京海淀区101中学温泉校区初三其他）如图，抛物线2815y x x =-+与x 轴交于A 、B 两点，对称轴

与x 轴交于点C ，点(0,2)D -，点(0,6)E -，点P 是平面内一动点，且满足90DPE ∠=?，M 是线段PB 的中点，连结CM ．则线段CM 的最大值是（）．

A ．3

B C ．

D ．5

27．（2019·河南省初三月考）如图所示，在DEF 中，10,6,8,EF DF DE ===以EF 的中点O 为圆心，作半圆与DE 相切，点A B 、分别是半圆和边DF 上的动点，连接,AB 则AB 的最大值与最小值的和是（）

A ．6

B ．1

C ．

D ．9

28．（2020·江苏省初三学业考试）如图，AB 是半圆O 的直径，点D 在半圆O 上，AB =，4=AD ，C 是弧BD 上的一个动点，连接AC ，过D 点作DH AC ⊥于H ，连接BH ，在点C 移动的过程中，BH 的最小值是（）

A ．6

B ．2

C ．2

D ．7

29．（2019·山东省初三二模）如图，直线334

y x =-+与x 轴、y 轴分别交于A 、B 两点，点P 是以C （﹣1，0）为圆

心，1为半径的圆上一点，连接PA ，PB ，则△PAB 面积的最小值是（） A ．5

B ．10

C ．15

D ．20

30．（2020·湖北省初三其他）如图，在等腰直角?ABC 中，斜边 AB 的长度为 8，以 AC 为直径作圆，点P 为半圆

上的动点，连接 BP ，取 BP 的中点 M ，则CM 的最小值为（）

A ．

B ．

D ．

31．（2020·西安市铁一中学初三二模）如图，在矩形ABCD 中，1AB =，AD =E 为BC 边上一动点，F 、

G 为AD 边上两个动点，且45FEG ∠=?，则线段FG 的长度最大值为__________．

32．（2020·山东省初三其他）如图，在Rt △ABC 中，∠C ＝90°，AC ＝4，AB ＝5，在线段AC 上有一动点P （P 不与C 重合），以PC 为直径作⊙O 交PB 于Q 点，连AQ ，则AQ 的最小值为___________、

33．（2020·江苏省初三一模）如图，在ABC ?中，10AB ＝，8AC ＝，6BC ＝，经过点 C 且与边 AB 相切的动圆与CA ，CB 分别相交于点P ，Q ，则线段PQ 长度的最小值是__________． 34．（2019·武汉外国语学校初三月考）如图所示,AB ＝6,AC ＝3,∠BAC ＝60°,为⊙O 上的一段弧,且∠BOC ＝

60°,分别在

、线段AB 和AC 上选取点P 、E 、F ,则PE ＋EF ＋FP 的最小值为__________

35．（2019·湖北省初三月考）如图，在平面直角坐标系中，等边AOB ?的边OB 在x 轴正半轴上，点()3,A a ，0a >，点D 、E 分别从B 、O 出发以相同的速度向O 、A 运动，连接AD 、BE 交于点F ，M 是y 轴上一点，则FM 的最小值为______. 36．（2019·盐城市泽夫初级中学初三月考）如图，已知正方形ABCD 的边长为4，以点A 为圆心，2为半径作圆，点E 是⊙A 上的任意一点，将点E 绕点D 按逆时针方向转转90°得到点F ，连接AF 、DF ，则1

AF DF 2

的最小值是__． 37．（2019·江苏省中考模拟）平面直角坐标系中，点A 、B 的坐标分别为（4，0）、（0，4），点D 为OB 上任意一点，连接AD ，以OD 为直径的圆交AD 于点E ，则当线段BE 的长最短时E 的坐标为_____．

38．（2020·吉林省初三其他）如图，在△ABC 中，∠C =45°，∠B =60°，BC +1，点P 为边AB 上一动点，过点P 作PD ⊥BC 于点D ，PE ⊥AC 于点E ，则DE 的最小值为_____． 39．（2020·重庆初一期末）如图，在平面直角坐标系中，以点A （0，2）为圆心，2为半径的圆交y 轴于点B ．已知点C （2，0），点D 为⊙A 上的一动点，以CD 为斜边，在CD 左侧作等腰直角三角形CDE ，连结BC ，则△BCE 面积的最小值为_____．

40．（2020·北京市八一中学初三月考）如图，

O 的半径为2．弦2AB =，点P 为优弧AB 上一动点，AC AP

⊥交直线PB 于点C ，则ABC 的最大面积是__________________．

参考答案1．D

2．C

3．B

4．A

5．C

6．C

7．D

8．D

9．A

10．A

11．3 4π

π+

3π-

．

15．π+6

．

18．262π

．

3 42π

20．π．21．A 22．B 23．A 24．B 25．A

26．C

27．D

28．A

29．A

30．C

．2

32．√73?3

33．4.8

．9

．6-

36．5

．2

39．4

．40

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2021中考英语超全试题分类汇编(含解析)

(2020最新模拟江苏省宿迁市 A) 根据句意及所给中文提示或英文解释，写出句中所缺单词。每小题1分) 46. My neighbours are very ▲ (友好的) to us. 47. Do you ▲ (同意) with what I say? 48. We had a very cold ▲ (冬季) last year. 49. Are you ▲ (有空的) this evening? 50. I can’t ▲ (买得起) to go to the 2020最新模拟 World Cup. 51. The tourists had no c ▲ but to wait for the next bus. 52. Tom is a ▲ (a good sense of humour) boy, so everyone likes him. 【答案】46.friendly 47.agree 48.winter 49.free 50.afford 51.choice 52.humo(u)rous (2020最新模拟.江苏省无锡市.B根据句意和汉语注释，在答题卡标有题号的横线上，写出单词的正确形式,每小题1 分） 6.Sometimes ______________（深厚的） feelings are hard to put into words. 7.Mr Wang was busy,but he_____________ （坚持） on seeing me off at the airport. 8.Will you join us in the _____________（讨论）about the teenage problems.

高考英语真题分类汇编各种题型全汇总

阅读理解专题一广告信息类 2018年 Passage 1 2018全国卷Ⅰ，6分话题：骑自行车在华盛顿特区观光词数：274 Washington,D.C. Bicycle Tours Cherry Blossom Bike Tour in Washington, D.C. Duration:3 hours This small group bike tour is a fantastic way to see the world-famous cherry trees with beautiful flowers of Washington, D.C. Your guide will provide a history lesson about the trees and the famous monuments where they blossom. Reserve your spot before availability —and the cherry blossoms — disappear! Washington Capital Monuments Bicycle Tour Duration:3 hours(4 miles) Join a guided bike tour and view some of the most popular monuments in Washington, D.C. Explore the monuments and memorials on the National Mall as your guide shares unique facts and history at each stop. Guided tour includes bike, helmet, cookies and bottled water. Capital City Bike Tour in Washington, D.C. Duration:3 hours Morning or Afternoon, this bike tour is the perfect tour for D.C. newcomers and locals looking to experience Washington, D.C. in a healthy way with minimum effort. Knowledgeable guides will entertain you with the most interesting stories about Presidents, Congress, memorials, and parks. Comfortable bikes and a smooth tour route(路线) make cycling between the sites fun and relaxing. Washington Capital Sites at Night Bicycle Tour Duration:3 hours(7 miles) Join a small group bike tour for an evening of exploration in the heart of Washington, D.C. Get up close to the monuments and memorials as you bike the sites of Capitol Hill and the National Mall. Frequent stops are made for photo taking as your guide offers unique facts and history. Tour includes bike, helmet, and bottled water. All riders are equipped with reflective vests and safety lights. 1. Which tour do you need to book in advance? A. Cherry Blossom Bike Tour in Washington, D.C. B. Washington Capital Monuments Bicycle Tour. C. Capital City Bike Tour in Washington, D.C. D. Washington Capital Sites at Night Bicycle Tour. 2. What will you do on the Capital City Bike Tour? A. Meet famous people. B. Go to a national park. C. Visit well-known museums. D. Enjoy interesting stories. 3. Which of the following does the bicycle tour at night provide? A. City maps. B. Cameras. C. Meals.

2018年中考英语真题分类汇编—冠词

1. （重庆A卷）I had egg and some milk for breakfast this morning. A. a B. an C. the D. / 2. （重庆B卷）I believe that apple a day keeps the doctor away. A. a B. an C. the D. / 3. （四川成都）—Who is boy playing soccer over there? —He is my classmate, Li Ping. A. a B. 不填 C. the 4. （天津）There is old piano in corner of the living room. A. an; the B. an; 不填 C. a; the D. a; a 5. （上海）Hurry up! The concert will begin in minute. A. a B. an C. the D. / 6. （山东临沂）The bed piano allows a music lover to play piano while he is lying in bed. A. a B. an C. / D. the 7. （山东青岛）We should have breakfast every day to keep healthy. A. a B. an C. / D. the 8. （江苏连云港）Zanco, American tech company, made tiniest phone in the world —the Tiny 11. A. the; a B. an; / C. /; a D. an; the 9. （宜宾）Every morning he spends hour doing exercise, then he goes to work. A. an; / B. a; a C. a; / 10. （随州）May is fifth month of the year. It’s very pleasant month. A. the; the B. the; a C. a; a D. the; / 11.（浙江温州）—Will you go to school-leavers’ party tomorrow? —Certainly. I’m going with my parents. A. a B. an C. the D. / 12. （甘肃白银）The man is driving at 40 kilometers hour. A. a B. an C. the D. / 13. （湖南郴州）—My daughter seldom has breakfast. —It’s unhealthy habit. Breakfast is very important to health. A. a B. an C. the 14. （山东东营）According to rule made in 2017, some kinds of dogs mustn’t be kept since May 1st, 2018 in Dongying. A. a B. an C. the D. / 15. （江苏宿迁）There will be talk on good manners at the school hall this afternoon. A. the B. an C. a D. / 16. （四川内江）—What time is it now, Mike? —It’s quarter past five. Let’s go to play basketball. A. 不填;不填 B. a; a C. the; a D. a; 不填 17. （哈尔滨）—What are you going to do next month? —I am going to travel to Germany, which is European country. A. a B. an C. the 18. （黑龙江绥化）I spend hour playing drums every day. A. a; the B. an; / C. an; the 19. （海南）Ann is my best friend. She can play piano very well.

2017中考英语真题分类汇编名词

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