The center of an inner Soddy circle. It has equivalent triangle center functions
(1)
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(2)
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where is the area of the triangle.
Given a point not between and , a detour of length
(3)
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is made walking from to via , the point is of equal detour if the three detours from one side to another via are equal. If has no angle , then the point given by the above trilinear coordinates is the unique equal detour point. Otherwise, the isoperimetric point is also equal detour.