29th International Mathematical Olympiad 1988 Problems & Solutions

A1.  Consider two coplanar circles of radii R > r with the same center. Let P be a fixed point on the smaller circle and B a variable point on the larger circle. The line BP meets the larger circle again at C. The perpendicular to BP at P meets the smaller circle again at A (if it is tangent to the circle at P, then A = P). (i)  Find the set of values of AB2 + BC2 + CA2. (ii)  Find the