In acute triangle $abc$, points $d$, $e$, and $f$ are located on sides $\overline{bc}$, $\overline{ac}$, and $\overline{ab}$ so that $\overline{ad} \perp \overline{bc}$, $\overline{de} \perp \overline{ac}$, and $\overline{df} \perp \overline{ab}$. let $r_1$ and $r_2$ be the radii of the circles around $\triangle abc$ and $\triangle aef$, respectively. determine the number of degrees in the measure of $\angle a$ if the area of $\triangle abc$ is equal to $r_1r_2$.