Question 165
Let $ABC$ be an acute triangle with $M$ is the midpoint of $BC$ and $\angle BAM \lt 90^\circ$, $\angle AMB = 60^\circ$. On ray $MA$, take the point $N$ such that $BN = AC$. Prove that $BC = 2AN$ and the orthocenters and circumcenters of two triangles $BMN$, $AMC$ form the four vertices of an isosceles trapezoid.