

Problem 525: Circles, Diameter, Tangent, Radius, Congruence, Measurement. Level: High School, SAT Prep, College geometry

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.


References:


Reference: Fukagawa Hidetoshi, Tony Rothman,
Sacred Mathematics: Japanese Temple Geometry
(Princenton
University Press, 2008).
Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life—samurai, farmers, and merchants—inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. 

Sangaku Problem 525, iPad apps.
Sangaku Japanese Geometry. 

Problem 526.
Equilateral Triangle, Chord, Measurement. 

Problem 524.
Circle, Equilateral Triangles, Midpoint, Side, Measurement. 

Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity. 

Problem 522.
Right Triangle, Circle, Diameter, Tangent. 








