如图,abc切圆o于点boa等于二角abc等于30度弦bc平行于oa,劣弧Bc的弧长为

Question

如图,abc切圆o于点boa等于二角abc等于30度弦bc平行于oa,劣弧Bc的弧长为

Answer 1

∵AB切圆O于B
∴OB⊥AB
∵AB＝3,OA＝2√3
∴cos∠A＝AB/OA＝√3/2
∴∠A＝30
∴∠AOB＝60,OB＝OA/2＝√3
∵BC∥OA
∴∠OBC＝∠AOB＝60
∵OC＝OB
∴∠OCB＝∠OBC＝60
∴∠BOC＝60
∴弧长BC＝π×2OB×60/360＝π×2√3×1/6＝√3π/3