# Relating The Orthocenter To The Circumcircle

Geometry Level 4

Let $$ABC$$ be an acute triangle with $$AB > BC$$. Let $$H$$ be the orthocenter (intersection of altitudes) of this triangle and $$M$$ be the midpoint of $$AC$$. The ray $$\overrightarrow{M H}$$ intersects the circumcircle of triangle $$ABC$$ at point $$P$$, where $$P$$ belongs to the minor arc $$BC$$. It is known that $$\angle ABP=90^{\circ}$$, $$MH=5$$ and $$HP=16$$. Find the length of $$BC$$.

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