Question 104
Let $ABC$ be a triangle such that $AB = 13$, $BC = 14$, $CA = 15$ and let $E, F$ be the feet of the altitudes from $B$ and $C$, respectively. Let the circumcircle of triangle $AEF$ be $\omega$. We draw three lines, tangent to the circumcircle of triangle $AEF$ at $A$, $E$, and $F$. Compute the area of the triangle these three lines determine.