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

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

Let $C1$ and $C2$ be concentric circles such that the diameter of $C1$ is $2 \mathrm{~cm}$ longer than that of $C2$. If a chord of $C1$ has length $6 \mathrm{~cm}$ and is a tangent of $C2$, then the diameter, in cm, of $C1$ is