Question

已知如图,A,B,C是圆O上的三个点,AD是∠BAC的平分线,交圆O于D,过B作圆O的切线交AD

Answer 1

∵AD平分∠BAC,∴∠BAD=∠CAD,∴BD=CD,

∵BE为切线,∴∠EBD=∠BAD(弦切角等于一所夹的弧所对的圆周角),

又∠E=∠E,

∴ΔEBD∽ΔEAB,

∴BE/AE=BD/AB,

∴AE*BD=AB*BE,

∴AE*CD=AB*BE.