All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the

Question

All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is

Accepted Answer

P 2 8 − 2 R 2 \frac{P^2}{8} - 2R^2 8 P 2 ​ − 2 R 2. A = l b A=lb A = l b l 2 + b 2 = 4 r 2 l^2+b^2=4r^2 l 2 + b 2 = 4 r 2 P = 2 ( l + b ) P\ =2\left(l+b\right) P = 2 ( l + b ) P 2 = l + b \frac{P}{2}=l+b 2 P ​ = l + b Squaring on both the sides, we get P 2 4 = l 2 + b 2 + 2 l b \frac{P^2}{4}=l^2+b^2+2lb 4 P 2 ​ = l 2 + b 2 + 2 l b P 2 4 = 4 r 2 + 2 l