Circumcircle Mid-Arc Triangle

The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle.

Its trilinear vertex matrix is

The following table gives the centers of the circumcircle mid-arc triangle in terms of the centers of the reference triangle for Kimberling centers with .

	center of circumcircle mid-arc triangle		center of reference triangle
	circumcenter		circumcenter
	orthocenter		incenter
	nine-point center		midpoint of incenter and circumcenter
	symmedian point		midpoint of and
	de Longchamps point		Bevan point
	perspector of abc and orthic-of-orthic triangle		external similitude center of circumcircle and incircle
	homothetic center of orthic and tangential triangles		midpoint of and
	Euler infinity point		isogonal conjugate of
	triangle centroid of orthic triangle		midpoint of and
	orthocenter of orthic triangle		midpoint of and
	symmedian point of orthic triangle		midpoint of incenter and symmedian point
	Kosnita point		Schiffler point
	isogonal conjugate of		-Ceva conjugate of
			anticomplement of Feuerbach point
	isogonal conjugate of		-isoconjugate of
	Tarry point		psi(incenter, symmedian point)
	Steiner point		antipode of