Question 40
Two circles with the same radius intersect at $X$ and $Y$. Let $P$ be a point on an arc $XY$ of a circle inside the other. Knowing that the segment $XY$ is long $3$ and that the angle $X\widehat{P}Y$ measures $120^\circ$, what is the area of the intersection between the two circles?
(A) $2\left(\pi-\frac{1}{4} \sqrt{3}\right)$
(B) $3(\pi-\sqrt{3})$
(C) $\frac{1}{2}(3 \pi-\sqrt{3})$
(D) $2\left(\pi-\frac{2}{3} \sqrt{3}\right)$
(E) $2\left(\pi-\frac{3}{4} \sqrt{3}\right)$.
(A) $2\left(\pi-\frac{1}{4} \sqrt{3}\right)$
(B) $3(\pi-\sqrt{3})$
(C) $\frac{1}{2}(3 \pi-\sqrt{3})$
(D) $2\left(\pi-\frac{2}{3} \sqrt{3}\right)$
(E) $2\left(\pi-\frac{3}{4} \sqrt{3}\right)$.