in triangle $abc$, $d$, $e$, and $f$ are the midpoints of sides $bc$, $ac$, and $ab$, respectively. let $bb'$ and $cc'$ be the angle bisectors. the line through $e$ perpendicular to $bb'$ intersects the line through $f$ perpendicular to $cc'$ at $p$. prove that $pd$ bisects $\angle edf$. hint(s): triangle $def$ is the medial triangle of triangle $abc$. there exists a homothety that takes triangle $abc$ to triangle $def$. what does this homothety do to the angle bisectors $bb'$ and $cc'$? what is the significance of point $p$ with respect to triangle $def$?