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When the outer Soddy circle has negative curvature, its center is the isoperimetric point of the triangle: the three triangles formed by this center and two vertices of the starting triangle all have the same perimeter. [4] Triangles whose outer Soddy circle degenerates to a straight line with curvature zero have been called "Soddyian triangles ...
In geometry, the isoperimetric point is a triangle center — a special point associated with a plane triangle.The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly in 1985 to denote a point P in the plane of a triangle ABC having the property that the triangles PBC, PCA, PAB have isoperimeters, that is, having the property that [1] [2]
Here the outer Soddy center lies outside the triangle. This analysis covers all cases in which four circles are externally tangent; one is always the inner Soddy circle of the other three. The cases in which one of the circles is internally tangent to the other three and forms their outer Soddy circle are similar.
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The Soddy line of a triangle is the line that goes through the centers of the two Soddy circles of that triangle. The Soddy line intersects the Euler line in the de Longchamps point and the Gergonne line in the Fletcher point. It is also perpendicular to the Gergonne line and together all three lines form the Euler-Gergonne-Soddy triangle. The ...
In the early days, the expression "new triangle geometry" referred to only the set of interesting objects associated with a triangle like the Lemoine point, Lemoine circle, Brocard circle and the Lemoine line. Later the theory of correspondences which was an offshoot of the theory of geometric transformations was developed to give coherence to ...
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