a MATHS

first you draw the circle with AB diameter
Now the area of the area composed by APB=πr^2/4
The area of APO=(1/2)r^2sin(180-2α)
The area composed by OPB=(2α/2π)(πr^2)
So area of APB=area of APO+area of OPB
πr^2/4=(1/2)r^2sin(180-2α)+(2α/2π)(πr^2)
πr^2/4=(1/2)r^2sin(2α)+(αr^2)
π/4=(1/2)sin(2α)+(α)
2α+sin2α = π/2
會考不是不考弧度了嗎?