Question 63
Let $\omega_{1}$ be a circle of radius $5$, and let $\omega_{2}$ be a circle of radius $2$ whose center lies on $\omega_{1}$. Let the two circles intersect at $A$ and $B$, and let the tangents to $\omega_{2}$ at $A$ and $B$ intersect at $P$. If the area of $\triangle ABP$ can be expressed as $\frac{a \sqrt{b}}{c}$, where $b$ is square-free and $a, c$ are relatively prime positive integers, compute $100a + 10b + c$.