Geometry Problem 41 with Solution: Sangaku, Mickey Mouse, Three Circles, Tangent, Radii, Chord, Tangency Points, Metric Relations

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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: .

Sangaku Mickey Mouse Geometry Problem

See solution below

Sketch and Typography of Problem 41

Sangaku Problem 41 Circle, Tangent, Measurement, Sketch and Typography

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.

Geometry Problem 41 with Solution: Sangaku, Mickey Mouse, Three Circles, Tangent, Radii, Chord, Tangency Points, Metric Relations

Sketch and Typography of Problem 41

Geometry Problem 41 Solution(s)