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Monge's Problem

\begin{figure}\begin{center}\BoxedEPSF{MongesProblem.epsf scaled 800}\end{center}\end{figure}

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

See also Circle Tangents, Radical Center


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

© 1996-9 Eric W. Weisstein