CAT (QA) PYQs

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

In a triangle $ABC, AB = AC = 8$cm. $A$ circle drawn with $BC$ as diameter passes through $A$. Another circle drawn with center at $A$ passes through $B$ and $C$. Then the area, in sq. cm, of the overlapping region between the two circles 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