# 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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