# Cyclic Quadrilaterals Geometry

**Geometry**Level 3

A circle with center \(O\) passes through the vertices \(A \) and \(C\) of triangle \(ABC\) and intersects segments \(AB\) and \(BC\) again at distinct points \(K\) and \(N\), respectively. The circumcircles of triangles \(ABC\) and \(KBN\) intersects at exactly two distinct points \(B\) and \(M\). What is the value of \(\angle OMB\)?