Friday, September 17, 2010
16th Balkan Mathematical Olympiad Problems 1999
16th Balkan Mathematical Olympiad Problems 1999A1. O is the circumcenter of the triangle ABC. XY is the diameter of the circumcircle perpendicular to BC. It meets BC at M. X is closer to M than Y. Z is the point on MY such that MZ = MX. W is the midpoint of AZ. Show that W lies on the circle through the midpoints of the sides of ABC. Show that MW is perpendicular to
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