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