Two Tangents

Geometry Level 3

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 $$AB+AC$$.

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