Question 84
Let $ABC$ be an acute triangle. Find the locus of the points $M$ in the interior of $\triangle ABC$ such that
$$
AB - FG = \frac{MF \cdot AG + MG \cdot BF}{CM}
$$
where $F$ and $G$ are the feet of the perpendiculars from $M$ to the lines $BC$ and $AC$, respectively.
$$
AB - FG = \frac{MF \cdot AG + MG \cdot BF}{CM}
$$
where $F$ and $G$ are the feet of the perpendiculars from $M$ to the lines $BC$ and $AC$, respectively.