Let k be a circumcircle of triangle ABC (AC<BC). Also, let CL be an angle bisector of angle ACB (LāAB), M be a midpoint of arc AB of circle k containing the point C, and let I be an incenter of a triangle ABC. Circle k cuts line MI at point K and circle with diameter CI at H. If the circumcircle of triangle CLK intersects AB again at T, prove that T, H and C are collinear.
. geometryincentercircumcirclearc midpointCyclicangle bisector