The perpendicular bisector to side AC of triangle ABC intersects side BC at point M (see fig.). The bisector of angle ∠AMB intersects the circumcircle of triangle ABC at point K. Prove that the line passing through the centers of the inscribed circles triangles AKM and BKM, perpendicular to the bisector of angle ∠AKB.
https://cdn.artofproblemsolving.com/attachments/b/4/b53ec7df0643a90b835f142d99c417a2a1dd45.png geometryincenterperpendicularangle bisector