26th International Mathematical Olympiad 1985 Problems & Solutions

A1.  A circle has center on the side AB of the cyclic quadrilateral ABCD. The other three sides are tangent to the circle. Prove that AD + BC = AB. A2.  Let n and k be relatively prime positive integers with k < n. Each number in the set M = {1, 2, 3, ... , n-1} is colored either blue or white. For each i in M, both i and n-i have the same color. For each i in M not equal to