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MN bisects segment CH

Source: JBMO Shortlist 2018 G1

July 22, 2019
geometrybisects segment

Problem Statement

Let HH be the orthocentre of an acute triangle ABCABC with BC>ACBC > AC, inscribed in a circle Γ\Gamma. The circle with centre CC and radius CBCB intersects Γ\Gamma at the point DD, which is on the arc ABAB not containing CC. The circle with centre CC and radius CACA intersects the segment CDCD at the point KK. The line parallel to BDBD through KK, intersects ABAB at point LL. If MM is the midpoint of ABAB and NN is the foot of the perpendicular from HH to CLCL, prove that the line MNMN bisects the segment CHCH.
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