如图,在△ABC中,AD、BD分别平分∠BAC和∠ABC,延长AD交△ABC的外接圆于E,连接BE.求证:BE=DE.

问题描述:

如图,在△ABC中,AD、BD分别平分∠BAC和∠ABC,延长AD交△ABC的外接圆于E,连接BE.求证:BE=DE.

证明:∠EBC=∠EAC(同弧所对圆周角相等).(2分)∵AD、BD分别平分∠BAC和∠ABC,∴∠BAE=∠EAC,∠DBC=∠ABD,(1分)∴∠EBC=∠BAE,(1分)∴∠EBC+∠DBC=∠BAE+∠ABD.又∵∠EBC+∠DBC=∠EBD(如图)∠BAE+∠A...