Question 70
In $\triangle ABC$, $\omega$ is the circumcircle, $I$ is the incenter and $I_{A}$ is the $A$-excenter. Let $M$ be the midpoint of arc $\widehat{BAC}$ on $\omega$, and suppose that $X, Y$ are the projections of $I$ onto $MI_{A}$ and $I_{A}$ onto $MI$, respectively. If $\triangle XYI_{A}$ is an equilateral triangle with side length $1$, compute the area of $\triangle ABC$.