Prove concyclic
2013-05-28 12:27 am
In the figure, chords AC and BD intersect at P. Chord CE intersects chords BD and AD at Q and R respectively. Given arc BC = arc CD, prove that A, P, Q and E are concyclic.
http://blog.yimg.com/3/29IKUtx7s59P5tXIOPy_taQBd4.VAjzdU2wdlP5k2kmK8P32zi9iuw--/35/l/pBRDMYO54xQQnsGESea2AQ.jpg
回答 (1)
2013-05-28 1:13 am
✔ 最佳答案
Join BE and CD and let ∠BDC = θ and ∠BDA = α as follows:圖片參考：http://i1191.photobucket.com/albums/z467/robert1973/May13/Crazy20_zps39f5c5eb.jpg
Then we have:
∠BEC = ∠DAC = ∠CAB = θ since arc BC = arc CD
∠BEA = ∠BDA = α (Angle in the same segment)
So ∠DPC = θ + α (Ext. ∠ of triangle)
Also with ∠AEQ = θ + α = ∠DPC, A, P, Q and E are concyclic.
參考: Myself
收錄日期: 2021-04-23 22:13:07
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130527000051KK00163