Question

如图,A是圆O外一点,OA=4,AB是圆O的切线,B为切点,且角BAO=30度,弦BC//OA,连接AC求阴影部分的面积

Answer 1

①∵ AB切⊙O于点B

∴ OB ⊥ AB 则∠ABO = 90°

又∠BAO = 30° ,OA = 4

∴ OB = 2 ∠AOB = 60° AB = 2√3 ②∵ CB∥OA ∴ ∠CBO = ∠AOB = 60°

又OB = OC

∴△COB为正三角形 则∠COB = 60°

③ S阴影 = S△AOB +S扇形OCB - S△AOC

= 1/2 · 2 · 2√3 + 60π·2²/360 - 1/2 · 2 · 4 · sin120°

= 2√3 + 2π/3 - 2√3

= 2π/3 【sin120° = sin60°】