CAT (QA) PYQs

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

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 $ABCD$ ?

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is