Question

已知：如图,△ABC是⊙O的内接等腰三角形,顶角∠BAC=36°,求证：五边形AEBCD是正五边形．

Answer 1

∵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．