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Part of 1987 IMO Longlists

Problems(1)

Find M such that B'C' is minimum

Source:

9/5/2010
Let ABCABC be a triangle. For every point MM belonging to segment BCBC we denote by B′B' and C′C' the orthogonal projections of MM on the straight lines ACAC and BCBC. Find points MM for which the length of segment B′C′B'C' is a minimum.
trigonometrygeometry unsolvedgeometry