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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