KöMaL 2019 C1576

A unit circle is centred at $O$, and $P$ is a point such that $OP=2$. Consider a secant through $P$ that intersects the circle at points $M$ and $N$ such that $M$ bisects the line segment $NP$. Prove that the area of triangle $OMN$ is smaller than $\frac{1}{2}$.