Problem

Source: Norwegian Mathematical Olympiad 1994 - Abel Competition p1b

Tags: geometry, angle bisector, equal segments, tangent



Let $C$ be a point on the extension of the diameter $AB$ of a circle. A line through $C$ is tangent to the circle at point $N$. The bisector of $\angle ACN$ meets the lines $AN$ and $BN$ at $P$ and $Q$ respectively. Prove that $PN = QN$.