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