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数学
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如图,△ABC是⊙O的内接三角形,AC=BC,D为⊙O中
AB
上一点,延长DA至点E,使CE=CD.
(1)求证:AE=BD;
(2)若AC⊥BC,求证:AD+BD=
2
CD.
人气:157 ℃ 时间:2019-08-18 18:39:09
解答
证明:(1)在△ABC中,∵AC=BC,∴∠CAB=∠CBA,∵∠CBA=∠CDE,(同弧上的圆周角相等),∴∠ACB=∠ECD,∴∠ACB-∠ACD=∠ECD-∠ACD,∴∠ACE=∠BCD.在△ACE和△BCD中,CE=CD∠ACE=∠AC=BCBCD,∴△ACE≌△BCD,...
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