CAT (QA) PYQs

On a triangle $A B C$, a circle with diameter $B C$ is drawn, intersecting $A B$ and $A C$ at points $P$ and $Q$, respectively. If the lengths of $A B, A C$, and $C P$ are $30 \mathrm{~cm}, 25 \mathrm{~cm}$, and $20 \mathrm{~cm}$ respectively, then the length of $BQ$ , in cm , 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

A circle is inscribed in a rhombus with diagonals $12 \mathrm{~cm}$ and $16 \mathrm{~cm}$. The ratio of the area of circle to the area of rhombus is