
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)
,
(2)
,
(3)
.
Reference: Fukagawa Hidetoshi, Tony Rothman,
Sacred Mathematics: Japanese Temple Geometry
(Princenton
University Press, 2008).
