在△ABC中,AD平分∠BAC,AD的垂直平分线交AD于E,交BC的延长线于F.∠B=40°,求∠CAF的度数.

∵AE=ED,∠ADF=∠DEF=90°,EF公共边∴△FED全等于△FEA∴∠FAE=∠FDE又∵∠FDE=∠B+∠BAD,∠FAE=∠CAF+∠CAD∴∠B+∠BAD=∠CAF+∠CAD∵AD平分∠BAC∴∠BAD=∠CAD∴∠CAF=∠B=40°