Problem

Problem of the Day #28 (Normal)

POTD Normal December 17, 2023
Author: excelex

A triangle $\triangle ABC$ is drawn with sides $AB = 13, BC = 14,$ and $AC = 15$ . Let $H$ be the orthocentre of $\triangle ABC$ and $M$ be the midpoint of side $AC$ . Point $D$ is drawn on line $HM$ such that $MD = MH$ . In other words, $D$ is the reflection of $H$ over $M$ . The length of $BD$ can be written as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Compute $m+n$ .

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Category: Problem of the Day
Points: 3
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