Question 200
In the triangle $ABC$, the excircle $C(I_a)$ relative to $BC$ is tangent to the straight lines $BC$, $CA$, $AB$ at $D$, $E$, respectively $F$. The angle bisector of $\angle BI_aC$ meets $BC$ at $M$ and $AM$ meets $EF$ at $P$. Prove that $DP$ is the angle bisector of $\angle FDE$.