Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle 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.

# Monge's Problem

## See also

Circle Tangent Line, Orthogonal Circles, Radical Center, Radical Circle## Explore with Wolfram|Alpha

## 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.

## Referenced on Wolfram|Alpha

Monge's Problem## Cite this as:

Weisstein, Eric W. "Monge's Problem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MongesProblem.html