5.2.4.29 Various problems on the plane

Condition: A circle is circumscribed around the triangle \( A B C \). The points \( M, N, K \) are respectively the midpoints of the arcs \( A B, B C, A C \), into which the points \( A, B, C \) divide the circle. Prove that the segments \( M N \) and \( B K \) are perpendicular.