The point S' which makes the perimeters of the triangles Δ B S' C, Δ C S' A, and Δ A S' B equal. The isoperimetric point exists iff a + b + c>4R + r, where a, b, and c are the side lengths of Δ A B C, r is the inradius, and R is the circumradius. The isoperimetric point is also the center of the outer Soddy circle of Δ A B C and has equivalent triangle center functions α | = | 1 - (2Δ)/(a(b + c - a)) α | = | sec(1/2 A) cos(1/2 B) cos(1/2 C) - 1.

equal detour point | perimeter | Soddy circles