Monge's Theorem

$\begin{figure}\begin{center}\BoxedEPSF{Monges_Theorem.epsf}\end{center}\end{figure}$

Draw three nonintersecting Circles in the plane, and the common tangent line for each pair of two. The points of intersection of the three pairs of tangent lines lie on a straight line.

References

Coxeter, H. S. M. ``The Problem of Apollonius.'' Amer. Math. Monthly 75, 5-15, 1968.

Graham, L. A. Problem 62 in Ingenious Mathematical Problems and Methods. New York: Dover, 1959. Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 115-117, 1990.

Walker, W. ``Monge's Theorem in Many Dimensions.'' Math. Gaz. 60, 185-188, 1976.