令AD,CE交于O,作OF平分∠AOC,交AC于F
∵∠ABC=60°
∴∠AOC=180°-1/2(∠BAC+∠BCA)=90°+1/2∠ABC=120°
∵OF平分∠AOC
∴∠AEO=∠AFO=∠CEO=∠CFO=60°
又,∠BAD=∠CAD,∠BCD=∠ACD,OA=OA,OC=OC
∴△AFO≌△AEO,△CFO≌△CDO
∴AF=AE,CF=CD
∴AC=AE+CD