Problem 41. Sangaku, Mickey Mouse, Circles, Tangent, Metric Relations. Level: High School, SAT Prep, College

The figure shows three circles (representing head and ears of Mickey Mouse) where a, b and c are respective radii, and d is the length of the exterior tangent. Prove that: .

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

Sangaku or San Gaku are Japanese geometrical problems in Euclidean geometry on wooden tablets created during the Edo period (1603-1867) by members of all social classes.

I have used Geometry Expressions to visualize these geometric forms and check out a variety of conjectures. Geometry Expressions is the world's first Interactive Symbolic Geometry System. This means: Geometric figures can be defined by either Symbolic Constraints or numeric locations.

You can download Geometry Expressions 2 Free Trial. It is a fully featured 30 day evaluation copy of the software. All constraints, constructions and measurements are available for you to use.