$M$ and $N$ are the midpoints of sides $BC$ and $AD$, respectively, of a square $ABCD$. $K$ is an arbitrary point on the extension of the diagonal $AC$ beyond $A$. The segment $KM$ intersects the side $AB$ at some point $L$. Prove that $\angle KNA = \angle LNA$. (5 points)
Problem
Source: Spring 2005 Tournament of Towns Junior O-Level #4
Tags: geometry, geometry unsolved, square, angle bisector