Question 7
Let $ABC$ be a triangle with $AB=13$, $BC=14$, and $CA=15$. Let $D$ be the foot of the altitude from $A$ to $BC$. The inscribed circles of triangles $ABD$ and $ACD$ are tangent to $AD$ at $P$ and $Q$, respectively, and are tangent to $BC$ at $X$ and $Y$, respectively. Let $PX$ and $QY$ meet at $Z$. Determine the area of triangle $XYZ$.