Question

AB为圆O直径，AD,BC,DC为圆O的切线，A,B,E是切点，AC,BD相交于F，AD=3,BC=5,求EF

求求各位啦~

Answer 1

∵AD⊥AB，BC⊥AB
∴AD‖BC
∴AD/BC＝DF/BF
∵AD＝DE，CE＝BC
∴DE/CE＝DF/BF
∴AD‖EF‖BC
∴EF/AD＝CE/CD，EF/BC＝DE/CD
两式相加得：
EF/AD＋EF/BC＝CE/CD＋DE/CD＝1
∴EF/3＋EF/5＝1
解得：EF＝15/8

Answer 2

CB=CE=5,DA=DE=3(切线长定理),
AD//BC,AD:BC=3:5=DF:FB=DE:EC.
EF//BC,EF:BC=3:8, EF=15/8