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CAT 2022 Slot 1 QA Question & Solution

GeometryMedium

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

Options

$\frac{P^2}{16} - R^2$
$\frac{P^2}{8} - 2R^2$
$\frac{P^2}{2} - 2PR$
$\frac{P^2}{8} - \frac{R^2}{2}$

Solution

Question Figure

$A=lb$

$l^2+b^2=4r^2$

$P\ =2\left(l+b\right)$

$\frac{P}{2}=l+b$

Squaring on both the sides, we get

$\frac{P^2}{4}=l^2+b^2+2lb$

$\frac{P^2}{4}=4r^2+2lb$

$\frac{P^2}{8}-2r^2=lb$

The answer is option B.