# A Pre-RMO question! -27

Geometry Level 2

Let $\overline{AH},\overline{AD}$ and $\overline{AM}$ be an altitude, an angle bisector, and a median of $\triangle ABC$. If $\overline{AB}=14$, $\overline{AC}=10$, $\overline{BC}=18$, and the area of $\triangle ADM$ is $\dfrac{7\sqrt{k}}{4}$, find value of $k$.

×