The points $K$ and $N$ lie on the hypotenuse $AB$ of a right triangle $ABC$. Prove that orthocenters the triangles $BCK$ and $ACN$ coincide if and only if $\frac{BN}{AK}=\tan^2 A.$
Problem
Source: 2016 XIX All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p1
Tags: geometry, orthocenter, right triangle, Ukrainian TYM