2026初中数学9年级上(苏科)第二章 对称图形-圆(单元测试培优卷)(解析版)

第二章对称图形——圆·培优卷





Ⅰ

!"#$10'()*30*(,'3*-

1#3*-#24-25./01·2345·6789-:;<=

>?@ABC(D*E#FGHI-

JHIKHLE(MNJCOPQRJEMN(>PSJTOU>BV?JWXMN(YZ[@J\①②

#-③④

A1BB2BC3BD4B



B

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^_@ACJ`abKIAcbCOPEJdef>PSTOJgh(i8jke1

lm?GJn

opMlm?qr*

s



①FtuHv1J>?wx@ABC(y>?$vz{=@A(|}~

②opKIAc(D*HIEJHI€KHLE([@~

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④>PSJTOG‡ˆKHD*vJ‰?(U>BV?JWXMN#ŠT‹CŒI-([@~

1([@J\②Ž④($2B

!

B

2#3*-#24-25./01·‘’“·”•-–—(JHIKHLE(=36°(z

J˜'G#-⊙푂퐴퐵퐶퐷∠퐶퐴퐵∠퐵퐶퐷

A72°B54°C36°D18°



C

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^KIAcbC™PAcNlm(JnGi8jkKIAcbC™PAcopK

IAcš›=(š›==36°(œ=ŠžŸ



⏜⏜

s

퐵퐶GHI(퐵퐷∠퐶퐴퐵(∠퐵퐴퐷∠퐵퐶퐷∠퐵퐴퐷

∵퐴퐵퐴퐵⊥퐶퐷

=(

⏜⏜

∴퐵퐶=퐵퐷=36°(

∴∠퐶퐴퐵=∠퐵퐴퐷(

∵∠퐵퐶퐷=36°∠퐵퐴퐷(

!

∴∠퐵퐶퐷C

3#3*-–—(GJHI(==(=38°(zJ¡¢G#-

퐴퐵⊙푂퐵퐶퐶퐷퐷퐸∠퐶푂퐷∠퐴퐸푂

A52°B57°C66°D78°



B

*

]

^£COPJdbC™PAcbN¤>PSJgh(¥opN£RNCOP¦U

1

===38°(z==114°(œopC™PAc¦U=2=57°(

§¨©ªNˆRNP«Šž∠퐷푂퐸∠퐵푂퐶∠퐶푂퐷∠퐵푂퐸3∠퐶푂퐷∠퐵퐴퐸∠퐵푂퐸

s



==(=38°(

=∵퐵퐶=퐶퐷=퐷퐸38°(∠퐶푂퐷

∴∠퐷푂퐸=∠퐵푂퐶=∠퐶푂퐷114°(

∴∠퐵푂퐸13∠퐶푂퐷

=2=57°(

∴∠퐵퐴퐸=(∠퐵푂퐸

∵푂퐴푂퐸==57°(

!

∴∠퐴퐸푂B∠퐵퐴퐸

4#3*-#2025·‘‘¬·­®¯°-–—(±JT‹C(ŒI(K²±?E(

==4(zJ³±#-⊙푂△퐴퐵퐶푂퐷⊥퐴퐵

∠퐶45°,푂퐸퐴퐵

A22B42C10D8



D

*

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^_>PSJT‹CTO(C™PAc(´µAc(KIAcNlm(i8¶ª·¸g

h¹ºšcG]Jn

C™PAcž¦=90°(N¤HP>PSJghž«

s



–—(»‹∠퐴푂퐵(

푂퐵

==45°(

∵∠퐴푂퐵=90°2∠퐶,∠퐶(

∴∠퐴푂퐵=(

∵푂퐵푂퐴±N¤HP>PS(

∴△퐴푂퐵(

∵푂퐸⊥=퐴퐵(

∴퐵퐸=퐴퐸4(

∵푂퐸==8(

∴!

퐴퐵D2푂퐸

5#3*-#2025·¼½¾5·­-tD¿HPÀÁdZ(ÂbÃÀÁıŢJ?ÆÇÅ?–—(ÈÅ

?A(B(C\`C£(–É`Hv·`C£MÊL?B(z·`HvžeËÈ#-

A?(0,3)B?(6,0)C?(1,3)D?(6,1)



C

*

ÌÍÎ

^_ÊvJghefKIAcŽÀÁ—SJgh(¦›Ï(

′

==1(Š¦›?JÀÁGŸ

JnopKIAcJgh¦›COQtÐÑ(œopÊv△퐵푂퐷≌△퐵퐸퐴

퐴퐸Jgh¦›(퐵퐷+퐸=90°ÏE?JÐъž

′

s



»‹∠푂퐵퐷(Ò∠퐸퐵퐴(JKHD*v(‰Ó?L?(z?ÔGQtCJCO(

′′

퐵퐶퐵퐶퐴퐵푂푂퐴퐶

>?ՃJCJCO±

(2,0)(

′

∴Ö\+=90°푂Ï(CMÊ(

′

∵ÌÏ(∠푂퐵퐷=∠퐸퐵퐴=퐵퐹(×====90°(

′′′′

∠퐵푂퐷∠퐸퐵퐴(ASA)(90°−∠퐴퐵푂퐴퐵푂퐷2,∠퐵퐴퐸∠퐵퐷푂

′

∴△퐵=푂퐷≌=△1퐵퐸퐴(z?JÀÁ±

(1,3)(

∴س퐴퐸퐵퐷(žlÈ?퐸(5,1)((7,0)(

?퐸퐵:;Ó?J»vZ(xفC£MÊJG

퐹퐺(1,3)((5,1)((7,0)

∴!

퐵C

6#3*-#2025·ÚÛÜÝ·­-–—([ވSJß`ˆ(MÊ(Ê?±?((

z±#-퐴퐵퐶퐷퐸퐴퐸퐶퐷⊙푂퐴퐶

∠퐴푂퐶

A108°B120°C135°D144°



D

*

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^_àˆSJáPAcbÊvJAâb>PSTPJgh(ã¥opàˆSJáPAc«

›[ވS,BáPJ¡¢±108°(opÊvJAâžl==90°(ä垦

==18°(œop>PSTPJgh«›∠푂퐶퐷J¡¢∠푂퐴퐸

∠퐵퐶푂s



–:—Qæ(»‹∠퐵퐴푂çسU?(∠퐴푂퐶

ވSG[ވS(퐵푂퐹

()×180°

∵퐴퐵퐶퐷퐸(

===5=108°

5−2

è∴∠퐵b∠퐵퐴퐸G∠퐵퐶퐷JÊv(

∵퐷퐶=퐸퐴⊙=푂90°(

∴∠푂퐶퐷=∠푂퐴퐸==18°(

∴∠퐵퐶푂=∠퐵퐴푂+108°−90°(=+(

∴∠퐶푂퐹=∠퐵퐶푂+∠퐶퐵푂+∠퐴푂퐹+∠퐵퐴푂=∠퐴퐵푂++=18°+108°+18°=144°

∠퐴푂퐶∠퐵퐶푂∠퐶퐵푂∠퐴퐵푂∠퐵퐴푂∠퐵퐶푂∠퐴퐵퐶∠퐵퐴푂

!

D

7#3*-#24-25./01·ÚÛéÚ·”•-–—(êˆSá‹L(=60°(

퐴퐵퐶퐷⊙푂∠퐴퐵퐶

=42°yJŒI±6(zJ³G#-

⏜

∠퐴퐶퐷⊙푂퐷퐶

1336

A3B5C5D2



πCπππ

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^_CJá‹êˆSJghbC™PAcb£³ëìb>PSáPŽAcNlm?(

i8jkC™PAcf£³ëìGJn

¥opCJá‹êˆSJghž¦

=120°(œop>PSáPŽAcž¦=18°(§¨¶ª

C™PAcž¦=36°(í¨op£³

îë슞∠퐴퐷퐶∠퐶퐴퐷

s



–—

»‹∠퐶푂퐷((

푂퐷푂퐶

êˆSá‹L(=60°(

∵=퐴퐵퐶퐷⊙=푂120°∠퐴퐵퐶(

∴∠퐴퐷퐶=42°180°−∠퐴퐵퐶(

∵∠퐴퐶퐷==18°(

∴∠퐶퐴퐷=180°−∠퐴퐷퐶−∠퐴퐶퐷=36°(

∴∠퐶푂퐷JŒI±2∠퐶퐴퐷6(

∵⊙푂36××66

J³±

180=5

⏜휋

∴!

퐷퐶C휋

8#3*-#24-25./0:·ïðñò·”Z-óôõöϔ¢

÷øÛtù.úìûüZýU_þ“J“ÿ

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⊙⊙

33

Jąëʱ2(yªCá‹[ęˆSÒāĄąë(ž¦πJąëʱ#-

A2B22C3D23



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^[àˆSŽC(HP>PS(«›[ęˆSJ¿Ē(Šž¦›ĚÉ

s



–—(±Cá‹[ęˆSZJBN¤>PS(Ò(

△퐴푂퐵퐴퐷⊥푂퐵

360°

ě(¦

==1(=8=45°(

푂퐴푂퐵2∠퐴푂퐵

=sin45°=2(

∴퐴퐷푂퐴⋅112

[ęˆSJ¿Ē±

8×2=8×2×1×2=22(

∴×1=22(Š

=2⋅푂퐵2~⋅퐴퐷

2

∴!휋B휋

9#3*-#2025·ĜĝĞğ·>­-–—(tRtZ(=90°(±Zv(y=10(

=24(ĠJáÊCŒI*ġ±△퐴퐵퐶((z∠퐵퐴퐶Jʱ#퐴퐷-퐴퐵

푟1

2

퐴퐶△퐴퐵퐷△퐴퐶퐷푟1푟2푟

37123725

A23B5C33D18



D

*

Ì

^_´µAc(HP>PSĢˆ1JZvNLĢˆJŒ(>PSJáÊCŽ¿Ē(Ġ

JáÊC±(bb*ġMÊL?bb(=90°(=10(=24△¦퐴퐵퐷

⊙퐼⊙퐼퐴퐵퐴퐷퐵퐷퐸퐹퐺∠퐵퐴퐶퐴퐵퐴퐶1

=26(=120(»‹bbbbb(++==60ž¦2×10

△퐴퐵퐶△퐴퐵퐼△퐴퐷퐼△퐵퐷퐼△퐴퐵퐷

퐵퐶126푆126퐼퐸퐼퐹퐼퐺10퐼퐴퐼퐵퐼퐷12푆푆푆푆

+2×2+2×2=60(Š¦=3(uc¦=5(¹åŠž«([@ģқĤĥvGJ

11112

n푟푟푟푟푟

s



ĠJáÊC±(bb*ġMÊL?bb(

△퐴퐵퐷⊙퐼⊙퐼퐴퐵퐴퐷퐵퐷퐸퐹퐺

=90°(=10(=24(

∵∠퐵퐴퐶퐴퐵퐴퐶

=+=10+24=26(

2222

∴퐵퐶1퐴퐵퐴퐶1

=2=2×10×24=120(

△퐴퐵퐶

푆±Ģˆ퐴퐵⋅1JZv(퐴퐶

∵퐴퐷퐵퐶1

===2=13(

∴퐴퐷퐵퐷퐶퐷1퐵퐶

==2=60(

△퐴퐵퐷△퐴퐶퐷△퐴퐵퐶

»‹∴푆(푆((푆(((z===(

퐼퐸+퐼퐹퐼퐺+퐼퐴퐼퐵=퐼퐷=퐼퐸60(×퐼퐹퐼퐺(푟1((

1△퐴퐵퐼푆△퐴퐷퐼126푆△퐵퐷퐼126푆△퐴퐵퐷

∵푆(퐴퐵⊥퐼퐸퐴퐷⊥퐼퐹퐵퐷⊥퐼퐺

2×10+2×2+2×2=60

111

∴푟10푟푟

¦

=3(

1

푟1126126

ucž¦(2×12+2×2+2×2=60(

222

12푟푟푟

¦=5(

21025

푟3

=12=18(

1

푟5

푟2

!

∴D

10#3*-#2020·ÚÛĦħ·­®¯°-–—(N¤JBĨPV?G1JBĩ?(

=90°(¤Ģˆ*ġ‰L?(*ġÈ?푅푡훥퐴퐵퐶ÒJÊv‰L?퐴⊙푂(×?ĪīG¤

∠퐴퐶퐵1J?(»‹퐴퐶(y퐴퐵JŒI±⊙푂4(z퐸,퐷Jí˜Ę±

#퐷,퐸⊙푂-퐹퐹퐵퐶

푂퐶,푂퐷,푂퐸⊙푂푂퐶

A25+2B42+2C6D8



A

*

¥N¤>PSJghbÊvJghfCJŒIMNĬAêˆSODFEG[ĂS(œ¦›?Cte

EF±HIJŒC1¶ĩ(zĭOCËȌCCOGÏ(OCJĘí˜(ª´µAcëì›OGJ³¡(œĮ

1CGJ³¡Šž

s



N¤RtABCZ(ACB=90°(

A=B=45°(∵△∠

∴∠DOE=2∠A=90°(

∴∠*ġÈ?∠D(EÒOJÊv(

∵ODDF(OEEF(⊙

∴êˆS⊥ODFE⊥GįS(

∴OD=OE=4(

∵êˆSODFEG[ĂS(

∴EF=4(

∴?FĪīG¤BC1J?(

∵ECF=90°

∴∠?CteEF±HIJŒC1¶ĩ(

∴

1

ĠEFJZ?±G(zEG=FG=CG=EF=2(×ĭOCËȌCCOGÏ(OCJĘí˜(ÌÏ(tRtOEGZ(

2

∴△

OG=+=4+2=25(

2222

OC=OG+CG=푂퐸퐸2퐺5+2.

∴±

A.

?İ

]

^_N¤>PSJghbÊvJghb[ĂSJĬAbHPQRJEGHIf´µAcN

lm?(i8jkMghfAcGJn.

ıIJij#$6'()*18*(,'3*-

11#3*-#24-25./01·ĶķĸHĹĺ0Ļз”•-–—(bbGJÊv(Ê?*ġG

PbCbDy=10(=6(zJ³G퐴퐵퐴퐶퐵퐷⊙푂

퐴퐵퐴퐶퐵퐷



4

*

由于、、是的切线，则=，=，求出的长即可求出的长．本题考

查了切线长定理，两次运用切线长定理并利用等式的性质是解题的关键．퐴퐵퐴퐶퐵퐷⊙푂퐴퐶퐴푃퐵푃퐵퐷퐵푃퐵퐷

s

解：、为的切线，

==6∵，퐴퐶퐴푃⊙푂

∴퐴퐶、퐴푃为的切线，

∵퐵푃=퐵퐷，⊙푂

∴퐵푃=퐵퐷===4．

故答案为：∴퐵퐷푃퐵4．퐴퐵−퐴푃10−6

12#3*-#24-25./0:·3ļ5·Ľ

-–—(GJHI(?C±C1?×

=22°(DGľ£JZ?(»‹((zJ¡¢±퐴퐵⊙푂

∠퐴퐵퐶퐵퐶퐵퐶퐶퐷∠퐵퐶퐷



34°/34¡

*

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^_C™PAc(KIAcJšĿ(HP>PSJßBĨPŀŁNlm?(i8jk

C™PAcfKIAcJšĿGJn

»‹‰L?(KIAcJšĿž¦(z=90°(HP>PSJßBĨPŀŁž¦

푂퐷퐵퐶퐸푂퐷⊥퐵퐶1∠푂퐸퐵

==68°(C™PAcž¦=2(ÌŠž«›J¡¢

s



–—(»‹∠퐵푂퐸90°−∠퐴퐵퐶‰L?(∠퐵퐶퐷∠퐵푂퐷∠퐵퐶퐷

푂퐷퐵퐶퐸

Gľ£JZ?(±CO(

∵퐷퐵퐶(푂

∴푂퐷⊥퐵퐶=90°(

∴∠푂퐸퐵=22°(

∵∠퐴퐵퐶===68°(

C™PAcž¦

∴∠퐵푂퐸90°−∠퐴퐵퐶90°−22°

11

=2=2×68°=34°(

±

∠퐵퐶퐷∠퐵푂퐷34°

13#3*-#2023·3·Z

ł-–—(GJHI(GJá‹>PSy

=(=4(zJHI=퐴퐷⊙푂△퐴퐵퐶⊙푂

∠퐷퐴퐶∠퐴퐵퐶퐴퐶⊙푂퐴퐷



42

*

»‹((optuCZHIQRJC™PG90°ž¦=90°(opC™PAcž¦

=퐶퐷(opCOP(E(£ćŃJdž¦푂퐶=(op´µAcŠž«∠퐴퐶퐷

∠퐶푂퐷s



»‹∠퐶푂퐴((–—

퐴퐶퐶퐷

퐶퐷푂퐶

GJHI(

∵퐴퐷⊙=푂90°(

∴∠퐴퐶퐷=(

∵∠퐷퐴퐶=∠퐴퐵퐶(

∴∠퐶푂퐷=(∠퐶푂퐴

è∴퐴퐶=퐶퐷4(

∵퐴퐶=4(

∴퐶퐷

tRtZ(=+=4+4=42(

2222

±

△퐴퐶퐷42퐴퐷퐴퐶퐶퐷

?İ

]

^_tuCZHIQRJC™PG90°(C™PAc(COP(E(£ćŃJd(´µA

c(i8jke1lmGJn

14#3*-#2025·¼½ń·>­-–—(GêˆSJT‹C(HvMÊL?B(

(=55°(zJ¡¢±⊙푂퐴퐵퐶퐷퐵퐸⊙푂

퐴퐶∥퐵퐸∠퐵퐴퐶∠퐴퐷퐶



110°

*

]

^_C™PAc(ÊvJgh(DºêˆSJgh(Cá‹êˆSJgh(»‹b(

¥opC™PAc¦==110°(z==35°(œopÊvJgh«›푂퐵푂퐶

=∠퐵푂퐶=55°(opDºvJgh¦2∠퐵퐴퐶∠푂퐵퐶∠푂퐶퐵==55°(z

∠퐵퐶퐸=∠푂퐵퐸−∠푂퐵퐶=70°(œopCá‹êˆSJghž«›∠퐴퐶퐵∠퐶퐵퐸J¡¢

∠퐴퐵퐶s



–—(»‹180°−∠퐵퐴퐶−∠퐴퐶퐵b(∠퐴퐷퐶

푂퐵푂퐶

=55°(

∵∠퐵퐴퐶==110°(

∴∠퐵푂퐶=2∠퐵퐴퐶(

∵푂퐵푂퐶

==2=35°(

180°−110°

∴Hv∠푂퐵퐶∠푂퐶퐵MÊL?B(

∵퐵퐸=90°⊙(푂

∴∠푂퐵퐸===55°(

∴∠퐵퐶퐸(∠푂퐵퐸−∠푂퐵퐶90°−35°

∵퐴퐶∥퐵퐸==55°(

∴∠퐴퐶퐵=∠퐶퐵퐸=70°(

∴∠퐴퐵퐶GêˆS180°−∠퐵퐴퐶−∠퐴퐶퐵JT‹C(

∵⊙푂=퐴퐵퐶퐷==110°

∴±

∠퐴퐷퐶180°−∠퐴퐵퐶110°180°−70°

15#3*-#2024·Ņņ³Ň·>­-ňˆ³±2J'[ĂSABCDŽˆ³±4J˜[ĂSEFGH–—ʼn

Ŋ(ŋ¦CbEß?Ōīōč(×BbCbH>?$v(ÌÏËÈAbFbG>?ÒBC(zCJŒI±



25

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^@ACJCO(ěžl(==2(===4(ŎJZ?(»‹

(((´µAcž¦===퐴퐵25(žl?퐵퐶퐶퐹±b퐶퐻b퐻퐺>?QÒCJCO(¹åž¦퐶퐻푂

푂퐴푂퐹푂퐺푂퐴푂퐹푂퐺푂퐴퐹퐺

s



ěžl(==2(===4(

ŎJZ?(z=퐴퐵=2(퐵퐶=4(퐶퐹퐶퐻퐻퐺

»‹퐶퐻(푂((푂퐶푂퐻푂퐵

푂퐴푂퐹푂퐺

´µAcž¦

=+=25(==25(

22

==(푂퐴퐴퐵푂퐵푂퐹푂퐺

∴Š

?푂퐴푂퐹±b푂퐺b>?QÒCJCO(

zCJŒI±푂퐴퐹2퐺5(

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25

16#3*-#24-25./01·ŏ5Őⷔ•-–—(êˆSá‹L(=15°(

==45°(+=2(zJŒI±

퐴퐵퐶퐷⊙푂∠퐴퐶퐷

∠퐵퐴퐶∠퐶퐴퐷퐴퐵퐴퐷⊙푂

6



3

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^_őN>PSJghĬA(C™PAc(N¤>PSJghĬANlm?(i8j

kC™PAcefőN>PSJghĬAGJn

»‹(سČ?(ŋ=(»‹çس‰L?(»‹(ŠžŒ¦(

¹åž«¦퐵퐷퐴퐵=2(œ©ªC™PAc¦U퐸퐵퐸퐴퐷퐶푂=60°⊙(¶ªœ푂퐹30°PJHP>PSJghŠž«퐴퐹△퐴퐷퐶≌△퐸퐵퐶

s



–—(»‹퐴퐶(سČ?(ŋ∠퐴퐹퐶=(»‹çس‰L?(»‹(

퐵퐷퐴퐵퐸퐵퐸퐴퐷퐶푂⊙푂퐹퐴퐹

êˆSá‹L(

∵+퐴퐵퐶퐷=⊙푂+=180°(

∴∠퐴퐷퐶=∠퐴퐵퐶(∠퐴퐵퐶∠퐶퐵퐸

∴∠퐴퐷퐶=∠퐶퐵퐸=45°(

∵∠퐵퐴퐶=∠퐶퐴퐷=45°(=90°(

∴∠퐶퐵퐷G∠퐶퐷퐵JHI(∠퐷퐴퐵=90°(

∴퐵퐷⊙GN¤HP>PS(푂∠퐷퐶퐵

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∴퐷퐶=퐵퐶(∠퐶퐵퐷

∵퐵퐸퐴퐷(SAS)(

∴△퐴퐷퐶≌=△퐸퐵퐶(=(

∴∠퐴퐶퐷+∠퐸퐶퐵=2(퐴퐶퐶퐸

∵퐴퐵+퐴퐷==2(

è∴퐴퐵퐵퐸=90°퐴퐸(

∵∠퐷퐶퐵=90°(

∴∠퐴퐶퐸

GN¤HP>PS(=+=(

2222

∴△퐴퐶퐸2퐴퐸퐴퐶퐴퐸2퐴퐶

=2=2(

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∵퐶퐹=90°(

∴∠퐹퐴퐶==15°(

∵∠퐴퐵퐷=∠퐴퐶퐷=+=60°(

∴∠퐴퐹퐶=∠퐴퐵퐶30°,∠퐴퐵퐷∠퐷퐵퐶

∴∠퐴퐶퐹11

=2(+=2+(2)=

22

222

∴퐴퐹2퐶퐹6퐴퐹퐴퐶퐶퐹퐶퐹

=3(

∴퐶퐹16

==2=3

∵푂퐹푂퐶6퐶퐹

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3

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17#6*-#24-25./01·ŖŗŘ5·”•-–—(=(‰L?C(D(GŒI(×

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(1)«Œ

=

(2)y=퐴퐶8(퐵퐷=2(«JŒI



퐶퐷(1)ř퐸퐹⊙푂

(2)5

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^_KIAc(N¤>PSJgh(´µAcN,jkAcfgh(xª´µAc«G

Jn

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222

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s

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(GŒI(=

=(=(∵푂퐸⊥퐴퐵푂퐸푂퐴푂퐵

∴퐶퐹퐷퐹=퐴퐹퐵퐹

∴퐴퐹−퐶퐹=퐵퐹−퐷퐹

∴#퐴퐶2-

Ġ퐵퐷JŒIG(–—(»‹(

=8(⊙=푂2푟퐶푂

∵KIAc¦

퐶퐷퐸퐹==4(=

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=+

222

∵퐶푂=4퐶+퐹푂퐹

222

∴푟=5(푟−2)

∴푟JŒIG5.

∴18⊙#푂6*-#24-25./01·ïð½D·”•-–—(tZ(E=(L(L

⊙푂퐴퐷퐵퐶푂퐸⊥퐴퐵퐸푂퐻⊥퐵퐶퐻

(1)«Œ

=

(2)y퐴퐵JŒI±퐶퐷5(=8(«J³



⊙푂(1)ř퐶퐷푂퐸

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s

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Š∴퐴퐷=퐵퐷(퐵퐶퐵퐷

퐴퐵=퐶퐷~

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»‹퐶퐷(

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==8((

∵퐴퐵=퐶퐷=4푂퐸⊥퐴퐵

∴퐴퐸퐸퐵

==3

22

19∴푂퐸#8*-–—(tĻг¡±푂퐵−퐵퐸1J[ĂSśÓZð„HPÀÁd(`C£ËÈśÓ?bb(Ŝ

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=2+4=25=2+4=25=2+6=210(

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222

∵퐷퐴±HP>PS(퐷퐶퐴퐶=90°(

Š∴△퐴퐷퐶JŒI±25(∠퐴퐷퐶J¡¢±90°(

⊙퐷90××(25)∠퐴퐷퐶

2

扇形=360=

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20∴푆#퐴퐷퐶8*-#24-25./015휋·ħ‘Ţ5·”•-ţlĨPá‹L(?GJáO(»‹

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⊙푂퐷퐷퐵퐶푙

(1)«Œ

HvMÊ~

(2)yŒI±푙5⊙(푂=8»‹(«Œ

=



⊙푂(1)ř퐵퐶퐵퐷퐷퐼퐷퐵

(2)ř

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#1-ÎŒŚHvlMÊ(qŤpÊvJĬAAc#ËȌITť×KHLŒIJHvG

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=퐷퐼(¹å©ªN¤>PSĬA¦›ĚĿ퐷퐵퐵퐼

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∵퐼D*△퐴퐵퐶(

∴퐴퐷=∠퐵퐴퐶(

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∴퐵퐷퐷퐶

?GJZ?(

⌢

∴퐷퐵퐶(

∴Hv푂퐷⊥퐵퐶(

∵푙∥(퐵퐶

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∴푙⊙푂

#2-»‹(

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∴∠퐶퐵퐷=∠퐶퐴퐷=(

∴?∠퐵퐴퐷G∠퐶퐵퐷JáO(∠퐶퐴퐷

∵퐼D*△퐴퐵퐶(

∴퐵퐼=∠퐴퐵퐶(

∴∠퐴퐵퐼=∠퐶퐵퐼+(=+(

∵∠퐵퐼퐷=∠퐴퐵퐼(∠퐵퐴퐷∠퐼퐵퐷∠퐶퐵퐼∠퐶퐵퐷

∴∠퐵퐼퐷∠퐼퐵퐷

=~

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]

^_ÊvJĬAAc(>PSJáObC™PAc(N¤>PSJĬA(Ŭŭ¶ªCJg퐷퐼퐷퐵

h#£bPbEJd-b>PSáOghfÊvĬAAcGn

21#10*-–—([éˆSá‹L(ˆ³±2

퐴퐵퐶퐷퐸퐹⊙푂

(1)«JHIJ³~

(2)«⊙푂J¡¢퐴퐷



∠퐴퐷퐵(1)4

(2)30°

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#1-»‹(«›J¡¢(¦UGNˆ>PS(¦U==2(Šž¦›ĚÉ~

#2-opC™PAc(Šž¦›ĚÉ푂퐵∠퐴푂퐵△퐴푂퐵퐴푂퐴퐵

s

#1-

»‹

푂퐵

[éˆSá‹L(

∵360°퐴퐵퐶퐷퐸퐹⊙푂

=6=60°(

è∴∠퐴푂퐵=(

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∴△퐴푂퐵==2

∴퐴푂=퐴퐵=4

∴#퐴퐷2-

2퐴푂=(=60°

∵1퐴퐵퐴퐵∠퐴푂퐵

=2=30°

∴∠퐴퐷퐵∠퐴푂퐵

22#10*-#2025·3{Ů·ı­-–—(ů˜ŰJűŰvıMNJC£(YZßűŲćŃJųDWX

=40m(ŴSJŵ¡=10m

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ŵ¡±13.2m퐸(퐹=14mŹź,ƄĮŹƅ10Ɔ(żŽÔƇ:ƈ퐶0.1m(Ŝ

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1

#1-ĠŰűC£QtCJCO±?(»‹b(©ªKIAcž¦=2=20m(Ġ

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푂푄#2-ĠŰűC£QtCJCO±?푂푀푥△푂푃푀(»‹b(»‹‰푥L?(ě¦êˆSGįS(

푂푂퐸1퐸퐹푂퐶퐸퐹퐺퐴퐵퐹퐸

z\==14m(©ªKIAc¦U=2=7m(¹å©ª´µAc«›J³(ë잦Źź

ƃ›ų¿Ÿ*Jŵ¡ŨFƌÈ퐸퐹퐴퐵12m(œĚ菟ƃ›ų¿Ÿ*JƍƎŵ¡퐸퐺퐸퐹13.2m(ƏƐ˜'¦›qÎýŠƄ푂퐺

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s

#1-

–—(ĠŰűC£QtCJCO±?(»‹b(

푂푂푀푂푄

ě¦((==40m(==10m(

1푂푄⊥1푀푁푀푁퐿푃푄푆

=2=2×40=20m(

Ġ∴푀푃=푀푁=m(z==()m(

푂푄푂푀푥푂푃푂푄−푃푄푥−10

tRtZ(+=(

222

∵(△)푂푃푀+20=푂푃(푀푃푂푀

222

¦

∴푥−10=25(푥

ŰűC£QtCJŒI±푥25m

#∴2-

–—(ĠŰűC£QtCJCO±?(»‹b(»‹‰L?(

푂푂퐸퐸퐹푂퐶퐸퐹퐺

ě¦(êˆSGįS(

==14m퐴퐵퐹퐸(

∴퐸퐹퐴퐵(

∵푂퐶⊥퐸퐹11

=2=2×14=7m(

#∴퐸퐺1-¦(퐸퐹==25m(

푂퐸푂퐶

==257=24m(

2222

∴푂퐺=푂퐸−퐸=퐺=−1m(

ÎſŒŹźÚőŦȘŰ(zŹźƃ›ų¿Ÿ*Jŵ¡ŨFƌÈ∴퐶퐺푂퐶−푂퐺25−24=12m(

13.2>12(15−1−2

∵qÎýŠƄĮŹƅ(

∴

ě¦(ČċqÎƄĮ0.1×10=120Ɔ(

13.2−12



ÎſŒŹźÚőŦȘŰ(qÎýŠƄĮŹƅ(ČċqÎƄĮ120