Question 41
Let $ABC$ be an equilateral triangle of side length $2$. Let $\omega$ be its circumcircle, and let $\omega_{A}$, $\omega_{B}$, $\omega_{C}$ be circles congruent to $\omega$ centered at each of its vertices. Let $R$ be the set of all points in the plane contained in exactly two of these four circles. What is the area of $R$?