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I wouldn't exactly call it trivial...

Source: German TST 2004, exam III

May 18, 2004
vectorgeometrygeometric transformationsimilar trianglesgeometry proposed

Problem Statement

Let ABCABC be an acute triangle, and let MM and NN be two points on the line ACAC such that the vectors MNMN and ACAC are identical. Let XX be the orthogonal projection of MM on BCBC, and let YY be the orthogonal projection of NN on ABAB. Finally, let HH be the orthocenter of triangle ABCABC. Show that the points BB, XX, HH, YY lie on one circle.
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