Circles (JEE 2003)

since OP=10 , sin(theta)=r/10 where theta belongs to (0,pi/2)

area = 1/2 x 2r x cos(theta) x (10-rsin(theta))

a= 10sin(theta)cos(theta)(10-10sin²theta))

a=100cos²thetaxsin(theta)xcos(theta)

da/dtheta =100[cos⁴(theta)-3sin²(theta)cos²(theta)}

=300cos⁴(theta)(1/√3-tan(theta))(1/√3+tan(theta))

a is maximum at theta =pi/6

r=10x1/2 = 5 units