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Soddy Circles Of A Triangle
In geometry, the Soddy circles of a triangle are two circles associated with any triangle in the plane. Their centers are the Soddy centers of the triangle. They are all named for Frederick Soddy, who rediscovered Descartes' theorem on the radii of mutually tangent quadruples of circles. Any triangle has three externally tangent circles centered at its vertices. Two more circles, its Soddy circles, are tangent to the three circles centered at the vertices; their centers are called Soddy centers. The line through the Soddy centers is the Soddy line of the triangle. These circles are related to many other notable features of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two. Construction Let A, B, C be the three vertices of a triangle, and let a, b, c be the lengths of the opposite sides, and s = \tfrac12(a + b + c) be the semiperimeter. Then the three circles centered at A, B, C have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outer Soddy Center As Equal Detour Point
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