Let a triangle $ABC$. $M$ is a point inside triangle. Construct the line through M perpendicular to $MA, MB, MC$ and intersect $BC, CA, AB $ at $A_0,B_0,C_0$ respectively. Prove that $A_0,B_0,C_0$ are collinear.
I really don't know where to start. Menelaus? Inversion?