Angles between Centers: 10602

Abstract

Editorial comment. When AABC is equilateral, the problem does not make sense, and when AABC is isosceles, the result follows readily from R > 2r. It is therefore appropriate to assume that AABC is scalene. All solutions submitted, including the proposers', were based on skillful manipulations of known results. References for these results include: Dan Sachelarie and Vlad Sachelarie, The Most Beautiful Problems of Mathematics, Teora Publishers, Bucharest, 1996; Trajan Lalesco, La Geometrie du Triangle, Vuibert, Paris, 1952; Emil Denath, Die merkwiirdigen Punkte des ebenen Dreiecks, VEB Deutscher Verlag der Wissenschaften, Berlin, 1976.