MathNet 2008-part-03 — 165 problems (EN–VI) Question 55

In the isosceles triangle $ABC$, $M$ is the middle point of the base $AB$. Let $N$ be a point from the leg $BC$, such that $MN \perp BC$ and $S$ be the middle point of the segment $MN$. Prove that $AN$ is perpendicular with $CS$.