A short time ago in Mathworld I came across
Amazingly, the difference between the areas of the outer and inner Napoleon triangles equals the area of the original triangle (Wells 1991, p. 156).
As Johnny Carson used to say 'I did not know that.'
But this is not the reason I write this post.
This fact is a fine raw material for P. theorem proof.
Maybe someone will take pains to prove that the sides
of squares equivalent in area to two Napoleons and the
referrence triangle make a right triangle.
Would make a nice addition to the list, would it not?