Inner Vecten Triangle

If the square is instead erected internally, their centers form a triangle that has (exact) trilinear vertex matrix given by

(1)

(E. Weisstein, Apr. 25, 2004).

The area of the inner Vecten triangle is

(2)

where is the area of the reference triangle. Its side lengths are

			(3)
			(4)
			(5)

The circumcircle of the inner Vecten triangle is the inner Vecten circle.

The following table gives the centers of the inner Vecten triangle in terms of the centers of the reference triangle for Kimberling centers with .

	center of inner Vecten triangle		center of reference triangle
	triangle centroid		triangle centroid
	circumcenter		complement of
	orthocenter		inner Vecten point
	de Longchamps point		anticomplement of

As in the exterior case, the triangles and are perspective with perspector at the inner Vecten point, which is Kimberling center .