CAT (QA) PYQs

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

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

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