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Line bisects altitude

Source: Moldova JTST 2017, problem 3

May 3, 2017
geometryprojective geometry

Problem Statement

Let ABCABC be a triangle inscribed in a semicircle with center OO and diameter BC.BC. Two tangent lines to the semicircle at AA and BB intersect at D.D. Prove that DCDC goes through the midpoint of the altitude AHAH of triangle ABC.ABC.
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