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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