# Geometry Problem 1081: Equilateral Triangle, Inscribed Circle, Inradius, Tangent Circles, Radius, Tangent Line, Sangaku Japanese Problem

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 C

_{1} touch each other as shown. Prove that: \((1)\, a = \dfrac{3}{5}r, \,(2)\, b = \dfrac{r}{5}, \,(3)\, c=\dfrac{r}{10}\).

Reference: Fukagawa Hidetoshi, Tony Rothman, Sacred Mathematics: Japanese Temple Geometry

(Princeton
University Press, 2008).

See also:

Poster and typography of problem 1081.

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