The Kiepert Point (Perspector) and Kiepert Triangle

Construct isosceles triangles with congruent base angles on each side of the triangle. The lines drawn from the vertex of each isosceles triangle to the opposite vertex AX, BY, and CZ are concurrent at the Kiepert Point. The three isosceles triangle vertex points form a triangle called the Kiepert Triangle. Triangles ABC and XYZ are in perspective, and the Kiepert point is also referred to as the Kiepert Perspector.