## POTW #25 - Oct. 7, 2024

#### Contributed by: bruhmoment

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#### Difficulty: 8

#### This problem is tagged with potw, potw2024.

**MCR Problem of the Week, Oct. 7, 2024 Edition**

In triangle $ABC$, $M$ is the midpoint of $BC$, and $D$ is the foot of the angle bisector from $A$. Given that $AM = BC = 26$ and $DM = 26/29$, find the area of triangle $ABC$ in the form $a \sqrt b$ such that $b$ is squarefree.
*Answer Submission Note(s)*

Type your answer in the form a*sqrt(b).

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