KöMaL 2007 A440

Given an isosceles triangle ABC such that the midpoint of base $BC$ is $M$, points $D$ and $E$ lie on sides $AB$ and $AC$, respectively, and $DE$ is parallel to $BC$. Choose two points, $P$ and $Q$ on the extensions of segment $BC$ beyond $B$ and $C$, respectively, such that $\frac 1{MP}+\frac 1{MQ} =\frac 1{MB}$ . Let $PD$ and $QE$ meet at $R$. What is the locus of point $R$?