3rd Chinese Mathematical Olympiad 1988 Problems & Solutions

A1.  a1, ... , an are reals, not all 0, such that there exist bi so that ∑1n bi(xi - ai) ≤ √(∑1n xi2) - √(∑1n ai2) for all real xi. Find the bi (in terms of the ai). A2.  ABCD is a cyclic quadrilateral. Its circumcircle has center O and radius R. The rays AB, BC, CD, DA meet the circle center O radius 2R at A', B', C', D' respectively. Show that A'B' + B'C' + C'D' + D'A' ≥ 2(