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Let H be the orthocenter of acute triangle ABC, and let M be the midpoint of \overline{AC}.  Ray MH intersects the circumcircle of triangle ABC at P.  If BC<AB, ABP=60, MH=14, and HP=3, then find length BC.

 

Note: The orthocenter of a triangle is the point where the altitudes of the triangle meet.

 
 Oct 29, 2024

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