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).
