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In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$  Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$  If $PQ = 36,$ $PM = 22,$ and $MY = 8,$ then find the area of triangle $PMY.$

 
 Nov 24, 2023

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