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 Center Function

**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.

© 1996-9

1999-05-26