

Problem
1103: Right Triangle, Incircle, Inscribed Circle,
Radius, Geometric Mean, Sangaku, Japanese, Metric Relations. Level: High School, SAT Prep, College
Geometry
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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}.

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