Given a triangle 
with inner and outer Soddy centers 
and 
, respectively, the inner Soddy triangle 
(respectively, outer Soddy triangle 
) is the triangle formed by the points of tangency
of the inner (respectively, outer) Soddy circle with the three mutually tangent circles
centered at each of the vertices of 
These triangles were explicitly mentioned but not named by Oldknow (1996). The name "Soddy triangles" is therefore proposed here for the first time.
