Question 72
We are given a triangle $ABC$ with incentre $I$. Suppose that there exists an intersection point $M$ of the line $AB$ and the perpendicular to $CI$ through $I$. Prove that the circumcircle of the triangle $ABC$ intersects the segment $CM$ in an interior point $N$ and that $NI \perp MC$.
(Peter Novotny)
(Peter Novotny)