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Intersection of segments on circumcircle

Source: Sharygin Geometry Olympiad 2012 - Problem 16

April 28, 2012
geometrycircumcirclegeometry unsolved

Problem Statement

Given right-angled triangle ABCABC with hypothenuse ABAB. Let MM be the midpoint of ABAB and OO be the center of circumcircle ω\omega of triangle CMBCMB. Line ACAC meets ω\omega for the second time in point KK. Segment KOKO meets the circumcircle of triangle ABCABC in point LL. Prove that segments ALAL and KMKM meet on the circumcircle of triangle ACMACM.
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