The Dao-Zeeman perspector of a line 
with respect to a reference
triangle 
is the homothetic center of 
and the congruent triangle
constructed below (Lozada 2024).
Let 
meet the sidelines 
, 
, and 
at distinct finite points 
, 
, and 
, respectively. Choose a point 
on 
distinct from those three points.
Let 
be the intersection of the line
through 
parallel to 
and the line through 
parallel to 
. Define 
and 
by cyclic permutation (Dao Thanh Oai 2016). The lines
through 
, 
, and 
in the directions of 
, 
, and 
, respectively, bound the image
of 
under a 
rotation about the perspector. The perspector lies on 
and is independent of 
(Lozada 2024).
If 
is the trilinear polar of the point
with barycentric coordinates 
, the perspector has barycentric
coordinates
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For the Euler line, the construction gives the Gossard perspector 
when the latter is defined (Lozada 2024).
