Relating The Orthocenter To The Circumcircle

Geometry Level 3

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

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