Question 135
Circle $\omega$ has radius $5$ and is centered at $O$. Point $A$ lies outside $\omega$ such that $OA = 13$. The two tangents to $\omega$ passing through $A$ are drawn, and points $B$ and $C$ are chosen on them (one on each tangent), such that line $BC$ is tangent to $\omega$ and $\omega$ lies outside triangle $ABC$. Compute $AB + AC$ given that $BC = 7$.