# A median and an altitude

Geometry Level pending

$$\triangle ABC$$ has side lengths $$|AB|=3$$, $$|BC|=7$$, and $$|AC|=8$$. Let $$E$$ be the midpoint of $$AC$$. The altitude from $$A$$ to $$BC$$ and the median from $$B$$ to $$AC$$ cut each other at $$X$$. Find $$m+n$$ if $$\dfrac{|BX|}{|XE|}$$ can be expressed as $$\dfrac {m}{n}$$, where $$m$$ and $$n$$ are coprime positive integers.

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