Two Tangents

Circle $\omega$ has a 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 the line $BC$ is tangent to $\omega$ and $\omega$ lies outside the triangle $ABC$ . Given that $BC=7$ , compute $AB+AC$ .