Question 105
Let $\triangle ABC$ be an acute triangle and $P$ be an inner point of $\triangle ABC$. Let $K$, $L$ and $M$ be the reflections of $P$ across $BC$, $AC$ and $AB$, respectively. Let $D$ and $E$ be the second points of intersection of $\odot(PBC)$ with lines $AB$ and $AC$, respectively. Let lines $MD$ and $LE$ intersect at $F$. Prove that $F$, $A$ and $K$ are collinear.