如图所示,圆o的弦ab,cd交于点p,ab=cd,求证:op平分角bpd

Question

如图所示,圆o的弦ab,cd交于点p,ab=cd,求证:op平分角bpd

Answer 1

证明：边点O作OM⊥AB于M,ON⊥CD于N,连接OB、OD
∵OM⊥AB
∴BM＝AB/2
∴OM＝OB-BM＝OB-AB/4
∵ON⊥CD
∴DN＝CD/2
∴ON＝OD-DN＝OD-CD/4
∵OB＝OD,AB＝CD
∴OM＝ON
∴OM＝ON
∴OP平分∠BPD
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