Problem

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

Tags: geometry, angles



Points M, N, P and Q are midpoints of the sides AB, BC, CD and DA of the inscribed quadrilateral ABCD with intersection point O of its diagonals. Let K be the second intersection point of the circumscribed circles of MOQ and NOP. Prove that OKAC.