Question 78
Alice draws a heart in her maths notebook as follows: first she draws two circles of radius $1~\mathrm{cm}$ with centres $O_1$, $O_2$, externally tangent to each other. Calling $r$ the common tangent to the two circles through the point of contact, she then chooses a point $P$ on $r$ such that $\widehat{O_1 P O_2}=60^\circ$ and draws the tangents to the two circles passing through $P$. What is the area of the resulting heart (that is, the shaded area in the figure) in $\mathrm{cm}^2$?
(A) $2 \sqrt{3}+\frac{4}{3} \pi$
(B) $\sqrt{3}+\pi$
(C) $\frac{7}{3} \pi$
(D) $\frac{3}{2}+2 \pi$
(E) None of the above
(A) $2 \sqrt{3}+\frac{4}{3} \pi$
(B) $\sqrt{3}+\pi$
(C) $\frac{7}{3} \pi$
(D) $\frac{3}{2}+2 \pi$
(E) None of the above