Consider three squares erected externally on the sides of a triangle . Call the centers of these squares , ,
and , respectively. Then the lines , , and concur in a point known as the
outer vecten point, which is Kimberling center. It has equivalent triangle
center functions
(1)
and
(2)
Now consider three squares erected internally on the sides of the triangle. Call the centers of these squares , , and , respectively. Then the lines , , and concur in a point known as the
inner vecten point, which is Kimberling center. It has equivalent triangle
center functions
(3)
and
(4)
The nine-point center, outer vecten point , and inner vector point are collinear (J. Montes
Valderrama, pers. comm., R. Barroso Campos, Apr. 20, 2004).
. Call the centers of these squares 
, 
,
and 
, respectively. Then the lines 
, 
, and 
concur in a point known as the
outer vecten point, which is Kimberling center 
. It has equivalent triangle
center functions
, 
, and 
, respectively. Then the lines 
, 
, and 
concur in a point known as the
inner vecten point, which is Kimberling center 
. It has equivalent triangle
center functions
, outer vecten point 
, and inner vector point 
are collinear (J. Montes
Valderrama, pers. comm., R. Barroso Campos, Apr. 20, 2004).
