Theorem of the Equal Incircles

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Take three adjacent triangles with a common base that have incircles with the same radius. Then the incircles of both double triangles also have the same radius. With four or more triangles, the equality propagates sidewards and upwards, so as to pile up in a pyramid of incircles, all equal in the same horizontal layer.

Contributed by: Claude Fabre (March 2011)
Open content licensed under CC BY-NC-SA


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Details

D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, 1991 p. 67.



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