MathNet 2019-part-04 — 184 problems (EN–VI) Question 35

Let $ABC$ be an isosceles triangle with $AC = BC$. Let $M$ be the midpoint of side $AB$, $N$ the foot of the perpendicular from $M$ to $AC$, and $P$ the midpoint of segment $MN$. Prove that the lines $BN$ and $CP$ are perpendicular.