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 O_{1} (radius r_{1}) is inscribed in
quadrilateral AFOE and circle O_{2} (radius r_{2}) is inscribed in
quadrilateral CDOE. Prove that r^{2} = 2r_{1}.r_{2}.
See also:
Art and typography of problem 1103.
