Monge's Problem

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Draw a Circle that cuts three given Circles Perpendicularly. The solution is obtained by drawing the Radical Center of the given three Circles. If it lies outside the three Circles, then the Circle with center and Radius formed by the tangent from to one of the given Circles intersects the given Circles perpendicularly. Otherwise, if lies inside one of the circles, the problem is unsolvable.

See also Circle Tangents, Radical Center

References

Dörrie, H. ``Monge's Problem.'' §31 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 151-154, 1965.