Radical Circle of Three Circles
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The radical circle of three circles has center at the radical center and is orthogonal to each of the three circles.[more]
Let the centers of the circles form the triangle and let its side lengths be , , .
Using Conway triangle notation, define
Half the triangle's area is then given by
In those terms, suppose the Cartesian coordinates of three centers are at , , and the corresponding radii are , , .
Then the radical circle of the three circles , , is the circle , where
Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA
Exercise: verify that the side lengths are indeed , , from the coordinates of the vertices.