MathNet 2020 — Math Olympiad Vault — Part 01 Question 144

Given is a parallelogram $ABCD$ with $\angle A \lt 90^\circ$ and $|AB| \lt |BC|$. The angular bisector of angle $A$ intersects side $BC$ in $M$ and intersects the extension of $DC$ in $N$. Point $O$ is the centre of the circle through $M$, $C$, and $N$.
Prove that $\angle OBC = \angle ODC$.