TOPICS

# Vecten Points

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).

Inner Vecten Triangle, Outer Vecten Triangle

## Explore with Wolfram|Alpha

More things to try:

## References

Pedret, J. M. "Problema 163." http://www.aloj.us.es/rbarroso/trianguloscabri/sol/sol163ped.htm.van Lamoen, F. "Vierkanten in een driehoek: 1. Omgeschreven vierkanten." http://home.wxs.nl/~lamoen/wiskunde/vierkant.html.van Lamoen, F. "Friendship Among Triangle Centers." Forum Geom. 1, 1-6, 2001.Yiu, P. "Squares Erected on the Sides of a Triangle." http://www.math.fau.edu/yiu/bottema38.pdf.Yiu, P. "On the Squares Erected Externally on the Sides of a Triangle." http://www.math.fau.edu/yiu/square.pdf.

Vecten Points

## Cite this as:

Weisstein, Eric W. "Vecten Points." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VectenPoints.html