(1)首先证明∠AEB=∠ACB=∠ABC=∠CED,证得△ABE≌△CDE.
(2)证明△AEF∽△DEC,推出=即可求得EF的长.
(1)证明:∵四边形ABCE为圆O的内接四边形,
∴∠ABC=∠CED,∠DCE=∠BAE,
又AB=AC,∴∠ABC=∠ACB,
∴∠CED=∠ACB,
又∠AEB和∠ACB都为所对的圆周角,
∴∠AEB=∠ACB,
∴∠CED=∠AEB,
∵AB=AC,CD=AC,
∴AB=CD,
在△ABE和△CDE中,
,
∴△ABE≌△CDE(AAS).
(2)【解析】
∵△ABE≌△CDE,
∴AE=EC=6,ED=BE=9,
即=,且∠AEB=∠CED,
∴△AEF∽△DEC,
∴=.
∴EF==4.