Around the acute-angled triangle ABC (AC>CB) a circle is circumscribed, and the point N is midpoint of the arc ACB of this circle. Let the points A1 and B1 be the feet of perpendiculars on the straight line NC, drawn from points A and B respectively (segment NC lies inside the segment A1B1). Altitude A1A2 of triangle A1AC and altitude B1B2 of triangle B1BC intersect at a point K . Prove that ∠A1KN=∠B1KM, where M is midpoint of the segment A2B2 . geometryequal anglescircumcircle