Question 71
Let $\triangle ABC$ be an acute triangle, with $M$ being the midpoint of $\overline{BC}$, such that $AM = BC$. Let $D$ and $E$ be the intersection of the internal angle bisectors of $\angle AMB$ and $\angle AMC$ with $AB$ and $AC$, respectively. Find the ratio of the area of $\triangle DME$ to the area of $\triangle ABC$.