Question 7
Let $AB$ be a diameter of a circle $\omega$ with center $O$ and $OC$ be a radius of $\omega$ which is perpendicular to $AB$. Let $M$ be a point on the line segment $OC$. Let $N$ be the second point of intersection of the line $AM$ with $\omega$, and let $P$ be the point of intersection of the lines tangent to $\omega$ at $N$ and at $B$. Show that the points $M, O, P, N$ are concyclic.