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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 O1 (radius r1) is inscribed in quadrilateral AFOE and circle O2 (radius r2) is inscribed in quadrilateral CDOE. Prove that r2 = 2r1.r2.


 

Problem 1103: Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, Sangaku, Japanese, Metric Relations


 

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Last updated: Mar 25, 2015, by Antonio Gutierrez