Question

已知如图三角形abc内接于圆o,ad垂直bc于d,弦bh垂直ac于e,交ad于f 求证：fe=eh

Answer 1

连接AH,

∵AD⊥BC,∴∠C+∠EAF=90°,

∵BE⊥AC,∴∠H+∠EAH=90°,

∵∠C=∠H,

∴∠EAF=∠EAH,

∵AE=AE,∠AEF=∠AEH=90°,

∴ΔAEF≌ΔAEH,

∴EF=EH.