如图,△ABC是⊙O的内接等腰三角形,顶角∠BAC=36°,弦BD,CE分别平分∠ABC,∠ACB.求证：五边形AEBC

如图,△ABC是⊙O的内接等腰三角形,顶角∠BAC=36°,弦BD,CE分别平分∠ABC,∠ACB.求证：五边形AEBCD是正五边形.

∵AB=AC,
∴∠ABC=∠ACB,
又∵∠BAC=36°,
∴∠ABC=∠ACB=72°．
又∵BD、CE平分∠ABC、∠ACB．
∴∠BAC=∠BCE=∠ABE=∠ABD=∠DBC=36°,
∴AÊ=BÊ=BĈ=CD̂=DÂ．
易证五边形AEBCD为正五边形．