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2011 PUMaC Geometry A3

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September 24, 2019
geometry

Problem Statement

Let PQPQ and PRPR be tangents to a circle ω\omega with diameter ABAB so that A,Q,R,BA, Q, R, B lie on ω\omega in that order. Let HH be the projection of PP onto ABAB and let ARAR and PHPH intersect at SS. If ∠QPH=30∘\angle QPH = 30^{\circ} and ∠HPR=20∘\angle HPR = 20^\circ, find ∠ASQ\angle ASQ in degrees.
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