# Orthocenter and Parallelogram

Geometry Level 5

In triangle $$ABC$$ with $$AB=13, BC=14, CA=15$$ and orthocenter $$H,$$ let $$N$$ be the midpoint of $$AH$$ and let $$M$$ be a point such that $$BHCM$$ is a parallelogram. If $$MN$$ intersects $$BC$$ at $$P$$, then $$\dfrac{BP}{PC}=\dfrac{m}{n}$$ for some relatively prime positive integers $$m$$ and $$n$$. Find $$m+n$$.

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