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concurrent wanted, parallelogram, circumcircle (2015 Kyiv City MO 11.4)

Source:

September 3, 2020
geometryparallelogramcircumcircleconcurrencyconcurrent

Problem Statement

In the acute-angled triangle ABC ABC , the sides AB AB and BCBC have different lengths, and the extension of the median BM BM intersects the circumscribed circle at the point N N . On this circle we note such a point D D that ∠BDH=90∘ \angle BDH = 90 {} ^ \circ , where H H is the point of intersection of the altitudes of the triangle ABC ABC . The point KK is chosen so that ANCK ANCK is a parallelogram. Prove that the lines AC AC , KH KH and BD BD intersect at one point.
(Igor Nagel)
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