$A,B,C$ are three collinear points and $P$ is a point not in the line $AB$: $AFE,BFD$ and $CED$ are perpendiculars to $PA,PB,PC$ respectively. Prove that $P,D,E,F$ are concyclic.
I attempted to do this using angle chasing. But I can't really understand why the lines are being defined by 3 points, since in my diagrams, this is simply not happening. So I need some help with this.