CAT (QA) PYQs

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 $ABCD$ ?

In a circle with center $C$ and radius $6\sqrt{2}$ cm, $PQ$ and $SR$ are two parallel chords separated by one of the diameters. If $\angle PQC = 45^\circ$, and the ratio of the perpendicular distance of $PQ$ and $SR$ from $C$ is $3:2$, then the area, in sq. cm, of the quadrilateral $PQRS$ is

Two tangents drawn from a point $P$ touch a circle with center $O$ at points $Q$ and $R$. Points $A$ and $B$ lie on $PQ$ and $PR$, respectively, such that $AB$ is also a tangent to the same circle. If $\angle AOB = 50^\circ$, then $\angle APB$, in degrees, equals