The inner García triangle of a reference triangle 
is obtained by reflecting its incenter 
in the perpendicular
bisectors of the three sides. Equivalently, it is obtained
by reflecting the vertices
of the outer García triangle across
the corresponding sidelines of 
(García 2014, 2016).
Writing 
,
,
and 
,
its 
-vertex has homogeneous barycentric
coordinates
 |
with the other two vertices obtained cyclically (Kimberling).
For a nonequilateral reference triangle, its circumcircle has the same circumcenter 
as 
and passes through 
(García 2014). Its circumradius
is therefore
 |
where 
and 
are the circumradius and inradius
of 
,
using the Euler triangle formula. In this
case, the inner García triangle is inversely
similar to 
with scale factor 
. For an equilateral
triangle, 
and all three constructed vertices coincide.
The García reflection triangle instead uses point reflections of the excenters in the side midpoints.
