Some Isochordic Circles Related to the Triangle

Extract

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, I₁, I₂, I₃ be the centres of the inscribed and escribed circles DEF, D₁E₁F₁, D₂E₂F₂, D₃E₃F₃.

Through A, B, C draw parallels to the opposite sides forming the triangle A₁B₁C₁, so that AA_l, BB₁, CC₁ are the medians of the triangle ABC, and there are then ten triangles like ABB₁, ACB₁, etc., of the same area.