Isoperimetric Point


The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff


where a, b, and c are the side lengths of DeltaABC, r is the inradius, and R is the circumradius. The isoperimetric point is also the center of the outer Soddy circle of DeltaABC and has equivalent triangle center functions


See also

Equal Detour Point, Perimeter, Soddy Circles

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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.", 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.

Referenced on Wolfram|Alpha

Isoperimetric Point

Cite this as:

Weisstein, Eric W. "Isoperimetric Point." From MathWorld--A Wolfram Web Resource.

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