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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 ...
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.
The equal detour point is the center of the inner Soddy circle of a triangle and the additional distance travelled by the detour is equal to the diameter of the inner Soddy Circle. [3] The barycentric coordinates of the equal detour point are [3]
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 ...
Pages in category "Circles defined for a triangle" The following 15 pages are in this category, out of 15 total. ... Sine-triple-angle circle; Soddy circles of a ...
Either Soddy circle, when taken together with the three given circles, produces a set of four circles that are mutually tangent at six points. The radii of these four circles are related by an equation known as Descartes' theorem. In a 1643 letter to Princess Elizabeth of Bohemia, [48] René Descartes showed that
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The Secrets of Triangles; Semiperimeter; Similarity (geometry) Sine-triple-angle circle; Soddy line; Sum of angles of a triangle; Surface triangulation; T. Triangle ...