△ABC中,角BAC=2角B,AB=2AC,AE平分角CAB,求证:AE=2CE
问题描述:
△ABC中,角BAC=2角B,AB=2AC,AE平分角CAB,求证:AE=2CE
答
∵∠BAC=2∠B(∠ABC),AE平分∠BAC,
∴∠CAE=∠BAE=∠ABC
∴∠CEA=∠BAC,
∵∠ACE=∠ACB,
∴△ACE∽△ABC,
∵AB=2AC,
∴AE=2CE