VTMO 2026 - Grade 9 - Final - SET 12 - Self-study Question 5

Let $ABCD$ be a parallelogram with $AB=2BC$ and $\angle DAB\gt 90^\circ$. Let $M$ be the midpoint of $DC$. Choose $K$ on line $AC$ such that $\angle MKC=\angle CKB$. The circumcircle of $DKM$ meets $AC$ again at $N$. Find $NA/NC$.