Taking ABC as the triangle of reference, with the usual notation for its sides and angles, let l = s − a, m = s− b, n = s − c. Let I, I 1, I 2, I 3 be the centres of the inscribed and escribed circles DEF, D 1 E 1 F 1, D 2 E 2 F 2, D 3 E 3 F 3.

Through A, B, C draw parallels to the opposite sides forming the triangle A 1 B 1 C 1, so that AA l, BB 1, CC 1 are the medians of the triangle ABC, and there are then ten triangles like ABB 1, ACB 1, etc., of the same area.