5.2.4.29 Various Problems on the Plane

Condition: around the triangle \ (a b c \) a circle is described. Points \ (m, n, k \), respectively, the middle of the arcs \ (a b, b c, a c \), into which points \ (a, b, c \) are divided. Prove that the segments \ (m n \) and \ (b k \) are perpendicular.