MathDB
2020 PUMaC Geometry A7

Source:

December 31, 2021
geometry

Problem Statement

Let ABCABC be a triangle with sides AB=34AB = 34, BC=15BC = 15, AC=35AC = 35 and let Γ\Gamma be the circle of smallest possible radius passing through AA tangent to BCBC. Let the second intersections of Γ\Gamma and sides ABAB, ACAC be the points X,YX, Y . Let the ray XYXY intersect the circumcircle of the triangle ABCABC at ZZ. If AZ=pqAZ =\frac{p}{q} for relatively prime integers pp and qq, find p+qp + q.
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