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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: 

References: H. Fukagawa & D. Pedoe "Japanese Temple Geometry Problems Sangaku" Winnipeg, Canada, 1989.

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.

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