VTMO 2026 - Grade 10 - Semifinal - SET 1 - Self-study Question 8

Let $ABCD$ be a convex quadrilateral with $\angle DAB=90^\circ$. Let $M,N$ be the respective midpoints of $BC,CD$, and suppose $\angle DAN=\angle NAM=\angle MAB$. Prove that $\angle DCB=60^\circ$.