Isoperimetric Point
The point 
which makes the Perimeters of the Triangles 
, 
,and 
equal. The isoperimetric point exists Iff the largest Angle of the triangle satisfies
or equivalently
where
, 
, and 
are the side lengths of 
, 
is the Inradius, and 
is the Circumradius.The isoperimetric point is also the center of the outer Soddy Circle of and has Triangle CenterFunction
See also Equal Detour Point, Perimeter, Soddy Circles
References
Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994. Kimberling, C. ``Isoperimetric Point and Equal Detour Point.''http://cedar.evansville.edu/~ck6/tcenters/recent/isoper.html. Kimberling, C. and Wagner, R. W. ``Problem E 3020 and Solution.'' Amer. Math. Monthly 93, 650-652, 1986. Veldkamp, G. R. ``The Isoperimetric Point and the Point(s) of Equal Detour.'' Amer. Math. Monthly 92, 546-558, 1985.
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