The Six-Fold Systems of Similar Circumscribed and Inscribed Triangles of a Given Triangle

Abstract

Let P be a point whose angle coordinates referred to a given triangle ABC are (λ,μ,γ) ; and let D, B, F be the centres of the circles BPC, CPA, APB. Then, if A'B'C' be any circumscribed triangle whose sides make© with those of DEF, the triangles A'B'C, DEF are similar, P being the centre of similinde and 2cosθ the ratio of similitude.