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perpendiculars from orthocenter, parallel lines lead to collinear

Source: Sharygin 2006 IX-XI CR 18

August 24, 2019
geometrycollinearparallelorthocenterprojections

Problem Statement

Two perpendicular lines are drawn through the orthocenter HH of triangle ABCABC, one of which intersects BCBC at point XX, and the other intersects ACAC at point YY. Lines AZ,BZAZ, BZ are parallel, respectively with HXHX and HYHY. Prove that the points X,Y,ZX, Y, Z lie on the same line.
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