In the triangle ABC, for which AC<AB<BC, on the sides AB and BC the points K and N were chosen, respectively, that KA=AC=CN. The lines AN and CK intersect at the point O. From the point O held the segment OM⊥AC (M∈AC) . Prove that the circles inscribed in triangles ABM and CBM are tangent.(Igor Nagel) geometryincircletangent circles