# 2015 UMO Problems/Problem 2

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## Problem

In $\triangle{ABC}, \overline{AC} = 13$ and $\overline{AB} = 20$, and the length of the altitude from $A$ to $\overline{BC}$ is $12$. If $M$ is the midpoint of $\overline{BC}$, find all possible length(s) of $\overline{AM}$, and demonstrate that these length(s) are achievable.