Question

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10 cm.

Answer 1

P is a point on the circumference of a circle of radius 

10 cm P = (10 cos α, 10 sin α) 

∴ PQ = 20 sinα and 

PS = 20 cos α 

A = area of PQRS = (20 sin α) (20 cos α) 

= 400 sin α cosc α 

= (200) (2 sin α cos α)

= 200 sin 2 α