Question

如图AO⊥BO,AO交圆O与D,AB交圆O与C,求证∠BOC=2∠A

Answer 1

1.作直径BE,连接CE,则∠BCE=90°

∴∠B+∠E=90°

∵AO⊥BO

∴∠B+∠A=90°

∴∠E=∠A

∵∠BOC=2∠E(圆周角定理)

∴∠BOC=2∠A