CAT (QA) PYQs

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

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

In a circle of radius $11$ cm, $CD$ is a diameter and $AB$ is a chord of length $20.5$ cm. If $AB$ and $CD$ intersect at a point $E$ inside the circle and $CE$ has length $7$ cm, then the difference of the lengths of $BE$ and $AE$, in cm, is