Vecten points
The outer and inner Vecten points differ according to whether the squares are extended outward from the triangle sides, or inward.
The Vecten points are named after an early 19th-century French mathematician named Vecten, who taught mathematics with Gergonne in Nîmes and published a study of the figure of three squares on the sides of a triangle in 1817.
On the sides BC, CA, AB of the triangle, construct outwardly drawn three squares with centres Oa, Ob, Oc respectively.
In Clark Kimberling's Encyclopedia of Triangle Centers, the outer Vecten point is denoted by X(485).
On the sides BC, CA, AB of the triangle, construct inwardly drawn three squares respectively with centres Ia, Ib, Ic respectively.
Reference triangle
△
ABC
Outer squares (centers at
O
a
, O
b
, O
c
)
Centerlines
AO
a
, BO
b
, CO
c
of outer squares (concur at
outer Vecten point
X
485
) and
nine-point circle
(centered at
nine-point center
X
5
)
Inner squares (centers at
I
a
, I
b
, I
c
)
Centerlines
AI
a
, BI
b
, CI
c
of inner squares (concur at
inner Vecten point
X
486
)