CAT (QA) PYQs

In a triangle $ABC, AB = AC = 8$cm. $A$ circle drawn with $BC$ as diameter passes through $A$. Another circle drawn with center at $A$ passes through $B$ and $C$. Then the area, in sq. cm, of the overlapping region between the two circles 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

Let $ABCD$ be a rectangle inscribed in a circle of radius $13 \mathrm{~cm}$. Which one of the following pairs can represent, in cm , the possible length and breadth of $ABCD$ ?