Let Soddy triangle , and
also let
The second Eppstein point (originally called the outer Oldknow point) is also the perspectors of a given triangle tangential
triangles of its inner Soddy Triangle (Oldknow
1996).
The second Eppstein point has equivalent triangle
center functions
where Kimberling center
See also First Eppstein Point ,
Soddy Circles ,
Soddy
Triangles
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References Danneels, E. "The Eppstein Centers and the Kenmotu Points." Forum Geom. 5 , 173-180, 2005. https://web.archive.org/web/20230207151943/https://forumgeom.fau.edu/FG2005volume5/FG200523index.html . Eppstein,
D. "Tangent Spheres and Triangle Centers." Amer. Math. Monthly 108 ,
63-66, 2001. Kimberling, C. "Encyclopedia of Triangle Centers: X(482)=2nd
Eppstein Point." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X482 . Oldknow,
A. "The Euler-Gergonne-Soddy Triangle of a Triangle." Amer. Math. Monthly 103 ,
319-329, 1996. Referenced on Wolfram|Alpha Second Eppstein Point
Cite this as:
Weisstein, Eric W. "Second Eppstein Point."
From MathWorld https://mathworld.wolfram.com/SecondEppsteinPoint.html
Subject classifications
,
,
and 
be the vertices of the inner Soddy triangle, and
also let 
,
,
and 
be the pairwise contact points of the three tangent circles. Then the lines 
, 
, and 
concur at a point known as the second Eppstein point
(Kimberling), denoted 
by Eppstein (2001). Although Eppstein (2001) actually cited
(Oldknow 1996), he missed the fact that 
is equivalent to the outer Oldknow point defined by Oldknow
(1996).
and the tangential
triangles of its inner Soddy Triangle (Oldknow
1996).
is the area of 
,
and is Kimberling center 
.
