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230问答网 > 怎样证明圆内接四边形的对角互补

怎样证明圆内接四边形的对角互补

2025-04-03 02:10:56

推荐回答（1个）

回答1：

方法一：直径对应的圆周角为直角四边形顶点ABCD,圆心O 连接AO延长交圆周于C',连接BC',DC' AC'是直径,∠ABC'=∠ADC'=90 ∠BAD+∠BC'D=180 ∠BC'D=∠BCD （对应相同的圆弧） ∠BAD+∠BCD=180 互补同理可以证明另两个角证法二：利用圆心角=圆周角*2 以弧BAD对应的圆心角为∠BOD ∠BCD=1/2*∠BOD ∠BAD=1/2*(360-∠BOD) ∠BAD+∠BCD=180 互补同理

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