Online Geometry Problems

Online Geometry Problem 1081: Equilateral Triangle, Inscribed Circle, Inradius, Tangent Circles, Radius, Tangent Line, Sangaku Japanese Problem. Level: High School, SAT Prep, College, Mathematics Education

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The figure below shows an equilateral triangle ABC with the inscribed circle of radius r, 3 yellows circles of radius a, 7 green circles of radius b, 6 white circles of radius c and circles C1 touch each other as shown.
Prove that (1) Formula to prove a, (2) Formula to prove b, (3) Formula to prove c.
 

Equilateral Triangle, Inscribed Circle, Inradius, Tangent Circles, Radius, Tangent Line, Sangaku Japanese Problem
 

Reference: Fukagawa Hidetoshi, Tony Rothman, Sacred Mathematics: Japanese Temple Geometry (Princenton University Press, 2008).

 

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Last updated: Feb 9, 2015