Theorem of the Equal Incircles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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



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

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.