Question 101
Let $ABC$ be an arbitrary triangle and $AMB$, $BNC$, $CKA$ regular triangles outward of $ABC$. Through the midpoint of $MN$ a perpendicular to $AC$ is constructed; similarly through the midpoints of $NK$ resp. $KM$ perpendiculars to $AB$ resp. $BC$ are constructed. Prove that these three perpendiculars intersect at the same point.