In a right triangle ABC (see the figure below)
incircle O (radius r) is tangent to BC, AC, and AB at D, E, and
F, respectively. Circle O1 (radius r1) is inscribed in
quadrilateral AFOE and circle O2 (radius r2) is inscribed in
quadrilateral CDOE. Prove that r2 = 2r1.r2.
Art and typography of problem 1103.