In a right triangle ABC with a right angle ∠C, n the sides AC and AB, the points M and N are selected, respectively, that CM=MN and ∠MNB=∠CBM. Let the point K be the projection of the point C on the segment MB. Prove that the line NK passes through the midpoint of the segment BC. (Alex Klurman) geometryright trianglebisects segmentequal segmentsequal angles