Given a triangles ABC and J_aJ_bJ_c, define point A₁ as the point in which the perpendicular to AB through the point J_b meets the perpendicular to AC through the point J_c, and similarly define B₁ and C₁. Then triangle A₁B₁C₁ is the hexyl triangle of triangle J_aJ_bJ_c wrt triangle ABC. If J_aJ_bJ_c is the Excentral Triangle, then A₁B₁C₁ is the ordinary Hexyl triangle.





Triangle J_aJ_bJ_c = Hexyl triangle wrt triangle ABC.