如图在圆O中,AB弧=CD弧,AD、BC相交于点E.求证（1）△ABD≌△CDB （2）OE平分角AEC

(1) 弧AB=弧CD,∴AB=AD,∠ADB=∠CBD
又∠BAD=∠DCB,∴△ABD≌△CDB
(2) 连接AO,CO,∵∠BAE=∠DCE,∠AEB=∠CED
且AB=CD,∴△ABE≌△CDE,∴AE=CE
又AO=CO,OE=OE,∴△AOE≌△COE
即∠AEO=∠CEO,∴OE平分∠AEC