Question

已知圆x2+y2=4,圆内定点P(1,0),过P点作两条互相垂直的弦AC和BD,设AC的倾斜角为α（0≤α＜π/2)

(1)求四边形ABCD的面积S (2)当S取最大值时,求α及最大面积

Answer 1

S = PAD的面积 + PCD的面积 + PAB的面积 + PBC的面积

= (1/2)AP*PD + (1/2)CP*PD + (1/2)AP*PB + (1/2)CP*BD

= (1/2)(AP + CP)PD + (1/2)(AP + CP)PB

= (1/2)AC*PD + (1/2)AC*PB)

= (1/2)AC(PD + PB)

= (1/2)AC*BD