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One more construction involving H and O

Source: VI Caucasus Mathematical Olympiad

March 14, 2021
geometryorthocenterCircumcenter

Problem Statement

An acute triangle ABCABC is given. Let ADAD be its altitude, let HH and OO be its orthocenter and its circumcenter, respectively. Let KK be the point on the segment AHAH with AK=HDAK=HD; let LL be the point on the segment CDCD with CL=DBCL=DB. Prove that line KLKL passes through OO.
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