CAT (QA) PYQs

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

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

Let $C$ be the circle $x^2 + y^2 + 4x - 6y - 3 = 0$ and $L$ be the locus of the point of intersection of a pair of tangents to $C$ with the angle between the two tangents equal to $60°$. Then, the point at which $L$ touches the line $x = 6$ is