The figure shows a line ABCD = d with
circles C_{1} of diameter AB and circle C_{2} of
diameter CD. AE and AF are tangent to circle C_{2}, DG
and DH are tangent to circle C_{1}. Circle C_{3}
of radius r_{3} is tangent to C_{1}, AE and AF
at B, K and L, respectively. Circle C_{4} of radius r_{4}
is tangent to C_{2}, DG and DH at C, N and P,
respectively. Prove that
.
See also:
Artwork Problem
525.
Reference: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008). |