Let $ABCD$ be a quadrilateral, with an inscribed circle with center $I$. Through $A$ are constructed perpendiculars to $AB$ and $AD$, which intersect $BI$ and $DI$ in points $M$ and $N$ respectively. Prove that $MN\perp AC$.
Problem
Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade
Tags: geometry