CAT (QA) PYQs

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

Let $C$ be a circle of radius $5$ meters having center at $O$. Let $P Q$ be a chord of $C$ that passes through points $A$ and $B$ where $A$ is located $4$ meters north of $O$ and $B$ is located $3$ meters east of $O$. Then, the length of $P Q$, in meters, is nearest to

In the XY-plane, the area, in sq. units, of the region defined by the inequalities $y \geq x+4$ and $-4 \leq x^{2}+y^{2}+4(x-y) \leq 0$ is