IMO 1959 Problem B1 Given the length |AC|, construct a triangle ABC with ∠ABC = 90 o , and the median BM satisfying BM 2 = AB·BC.
Area = AB·BC/2 (because ∠ABC = 90 o = BM 2 /2 (required) = AC 2 /8 (because BM = AM = MC), so B lies a distance AC/4 from AC. Take B as the intersection of a circle diameter AC with a line parallel to AC distance AC/4. s are also available in: Samuel L Greitzer, International Mathematical Olympiads 1959-1977, MAA 1978, and in István Reiman, International Mathematical Olympiad 1959-1999, ISBN 189-8855-48- X. 1st IMO 1959 home © John Scholes jscholes@kalva.demon.co.uk 17 Sep 1998 Last corrected/updated 24 Sep 2003