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

A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of the smaller region 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