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2023 Fall LMT Team #15 area of PQYX , (BCM), (BCN)

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February 4, 2024
geometry

Problem Statement

In triangle ABCABC with AB=26AB = 26, BC=28BC = 28, and CA=30C A = 30, let MM be the midpoint of ABAB and let NN be the midpoint of CAC A. The circumcircle of triangle BCMBCM intersects ACAC at X≠CX\ne C, and the circumcircle of triangle BCNBCN intersects ABAB at Y≠BY\ne B. Lines MXMX and NYNY intersect BCBC at PP and QQ, respectively. The area of quadrilateral PQYXPQY X can be expressed as pq\frac{p}{q} for positive integers pp and qq such that gcd(p,q)=1(p,q) = 1. Find qq.
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