

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: .
See
also:
Problem art
41
Sketch
art of problem
41

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 (16031867) 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.
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