USAMO problem, interesting

Geometry Level 5

If \(AB = 13, BC = 14, CA = 15\) where \(H, AP, X, Y\) are respectively orthocenter of \(ABC\), internal angle bisector of \(\angle BAC\), circumcenter of \(APB\), orthocenter of \(APC\);

Find value of \(24XY\).

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