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Tripolar Coordinates of Soddy Centers

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For a triangle , let , and be the side lengths, the circumradius, the inradius and the semiperimeter.

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Let and be the outer and inner Soddy centers.

Then

,

.

The formulas for distances to and are similar. These formulas thus provide three distances from the vertices to each center, which are its tripolar coordinates.

You can drag the points , and .

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Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA

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