CAT (QA) PYQs

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

On a rectangular metal sheet of area $135 \mathrm{sq}$ in, a circle is painted such that the circle touches two opposite sides. If the are the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

A chord of length $5 \mathrm{~cm}$ subtends an angle of $60^{\circ}$ at the centre of a circle. The length, in cm , of a chord that subtends an angle of $120^{\circ}$ at the centre of the same circle is