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Problem 6 Midpoint of segment

Source: PAMO 2017 Problem 6

July 5, 2017
geometryorthocentercircumcircle

Problem Statement

Let ABCABC be a triangle with HH its orthocenter. The circle with diameter [AC][AC] cuts the circumcircle of triangle ABHABH at KK. Prove that the point of intersection of the lines CKCK and BHBH is the midpoint of the segment [BH][BH]
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