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2007 Geometry #4: Tangents to a Circle

Source:

June 22, 2012
geometry

Problem Statement

Circle ω\omega has radius 55 and is centered at OO. Point AA lies outside ω\omega such that OA=13OA=13. The two tangents to ω\omega passing through AA are drawn, and points BB and CC are chosen on them (one on each tangent), such that line BCBC is tangent to ω\omega and ω\omega lies outside triangle ABCABC. Compute AB+ACAB+AC given that BC=7BC=7.
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