24th International Mathematical Olympiad 1983 Problems & Solutions

A1.  Find all functions f defined on the set of positive reals which take positive real values and satisfy:   f(x(f(y)) = yf(x) for all x, y; and f(x) → 0 as x → ∞. A2.  Let A be one of the two distinct points of intersection of two unequal coplanar circles C1 and C2 with centers O1 and O2 respectively. One of the common tangents to the circles touches C1 at P1 and C2 at P2,