Question 72
A circle $\omega_{1}$ of radius $15$ intersects a circle $\omega_{2}$ of radius $13$ at points $P$ and $Q$. Point $A$ is on line $PQ$ such that $P$ is between $A$ and $Q$. $R$ and $S$ are the points of tangency from $A$ to $\omega_{1}$ and $\omega_{2}$, respectively, such that the line $AS$ does not intersect $\omega_{1}$ and the line $AR$ does not intersect $\omega_{2}$. If $PQ = 24$ and $\angle RAS$ has a measure of $90^{\circ}$, compute the length of $AR$.