Question 49
Let $BM$ be a median in an acute triangle $ABC$, whose sides $AB$ and $BC$ have different length. The extension of $BM$ intersects the circumcircle of $ABC$ at a point $N$. Let $D$ be a point on the circumcircle such that $\angle BDH = 90^\circ$, where $H$ is the orthocenter of $ABC$. Let $K$ be a point chosen so that $ANCK$ is a parallelogram. Prove that the lines $AC$, $KH$ and $BD$ are concurrent.
(Ihor Nahel)
(Ihor Nahel)