15th International Mathematical Olympiad 1973 Problems & Solutions

A1.  OP1, OP2, ... , OP2n+1 are unit vectors in a plane. P1, P2, ... , P2n+1 all lie on the same side of a line through O. Prove that |OP1 + ... + OP2n+1| ≥ 1. A2.  Can we find a finite set of non-coplanar points, such that given any two points, A and B, there are two others, C and D, with the lines AB and CD parallel and distinct? A3.  a and b are real numbers

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