1 / 17

圓的弦線

O. R. P. Q. 圓的弦線. A. 圓的弦線. 定理 1 (p.124) 由圓心至弦的垂必平分該弦。 i.e. 如果 OR  PQ 那麼 PR = RQ 參考 : 圓心至弦的垂平分弦. O. R. P. Q. 證明 :. OP = OQ ( 半徑 ).  ORP =  ORQ = 90  ( 已知 ). OR = OR ( 相同邊 ). OPR  OQR (RHS). PR = RQ. O. R. P. =. =. Q. 定理 2 (p.124) 連接圓心和弦的中點的直必垂直於該弦。

devon
Download Presentation

圓的弦線

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. O R P Q 圓的弦線 A.圓的弦線 定理1 (p.124) 由圓心至弦的垂必平分該弦。 i.e. 如果OR  PQ 那麼PR = RQ 參考:圓心至弦的垂平分弦

  2. O R P Q 證明 : OP = OQ (半徑) ORP = ORQ = 90 (已知) OR = OR (相同邊) OPR OQR(RHS) PR = RQ

  3. O R P = = Q 定理 2 (p.124) 連接圓心和弦的中點的直必垂直於該弦。 i.e. 如果 PR = RQ 那麼OR  PQ 參考: 圓心至弦中點的連垂直弦

  4. O R P = = Q ORP +  ORP = 180 (直上的鄰角) 證明: OP = OQ (半徑) PR = RQ (已知) OR = OR (相同邊) POR QOR(SSS) ORP = ORP(同位角s ,  )   ORP =  ORP = 90 OR  PQ

  5. O R P = = Q 一條弦的垂直平分必通過圓心。

  6. D N C O M A B 定理3 (p.127) 等弦與圓心等距 i.e. 如果 AB=CD 那麼 OM = ON 參考:等弦與圓心等距

  7. D N C O M A B AB = CD (已知) AM=MB=1/2AB (圓心至弦的垂平分弦) CN=ND=1/2CD (圓心至弦的垂平分弦) AM=CN OA=OC (半徑) OMA = ONC= 90 (已知) OAM OCN(RHS) OM=ON (同位邊， )

  8. D N C O M A B 定理4 (p.127) 與圓心等距的弦等長 i.e. 如果 OM = OM 那麼 AB = CD 參考：與圓心等距的弦等長

  9. D N C O M A B OM = ON (已知) OA=OC (半徑) OMA = ONC= 90 (已知) OAM OCN(RHS) AM=CN (同位邊,  ) AM=MB=1/2AB (圓心至弦的垂平分弦) CN=ND=1/2CD (圓心至弦的垂平分弦) AB = CD

  10. 圓心角和圓周角 R R R Q Q O S S O O P P P Q S  弧AQB對向兩個角: POR -圓心角 PQR -圓周角

  11. R a Q b O S P 定理 5 (p.132) 圓心角兩倍於圓周角 i.e. 2a = b 參考圓心角兩倍於圓周角

  12. x m y n R O Q P OQ = OR (半徑) OQR = ORQ = x (等腰底角) m =2x(外角) 相似地, n = 2y a = n+ m = 2x +2y = 2b POR = 2PQR

  13. R Q S O x m P y n OQ = OR (半徑) OQR = ORQ = x (等腰內角) m =2x(外角) 相似地, n = 2y a = n+ m = 2x +2y = 2b POR = 2PQR

  14. R O R m P Q n O x y P Q OQ = OR (半徑) OQR = ORQ = x (等腰底角) m =2x(外角) 相似地, OQP = OPQ = y (等腰底角) n = 2y (ext.  of  ) a = n- m = 2y- 2x = 2b POR = 2PQR

  15. R Q P O 定理 6 (p.134) 半圓上的圓周角是直角 i.e. 如界 PQ是直徑， 那麼 PRQ= 90 參考: 圓周上的圓周角

  16. C x y A B 陰影部份ACB -主要弓形 x -弓形ACB上的角 x , y -在同一弓形上的角

  17. C x D y A B 定理 7 (p.136) 在同一弓形上的圓周角相同 i.e. 如果AB是弦, 那麼x = y 參考: 同弓形內的圓周角

More Related