CAT (QA) PYQs

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

A rectangle with the largest possible area is drawn inside a semicircle of radius $2$ cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

The vertices of a triangle are $(0,0)$, and $(4,0)$ and $(3,9)$. The area of the circle passing through these three points is