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2010 Geometry #10

Source:

January 2, 2024
geometry

Problem Statement

Circles ω1\omega_1 and ω2\omega_2 intersect at points AA and BB. Segment PQPQ is tangent to ω1\omega_1 at PP and to ω2\omega_2 at QQ, and AA is closer to PQPQ than BB. Point XX is on ω1\omega_1 such that PX∥QBPX\parallel QB, and point YY is on ω2\omega_2 such that QY∥PBQY\parallel PB. Given that ∠APQ=30∘\angle APQ=30^\circ and ∠PQA=15∘\angle PQA=15^\circ, find the ratio AX/AYAX/AY.
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