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Collinear points THC

Source: Bosnia and Herzegovina TST 2016 day 2 problem 2

May 16, 2016
geometryincentercircumcirclearc midpointCyclicangle bisector

Problem Statement

Let kk be a circumcircle of triangle ABCABC (AC<BC)(AC<BC). Also, let CLCL be an angle bisector of angle ACBACB (LāˆˆAB)(L \in AB), MM be a midpoint of arc ABAB of circle kk containing the point CC, and let II be an incenter of a triangle ABCABC. Circle kk cuts line MIMI at point KK and circle with diameter CICI at HH. If the circumcircle of triangle CLKCLK intersects ABAB again at TT, prove that TT, HH and CC are collinear. .
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