This is problem #31 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics[/i].
If the three given circles "box in" Monge's circle so that P cannot escape between two circles, P can be pushed inside the circles by increasing the radii or moving them closer together. Once P falls to the interior, there is no solution. _____ Monge's Problem: 1) [i]What is the locus of points with equal tangents to two circles? [/i][url]http://www.geogebratube.org/material/show/id/33873[/url] 2) Draw a Chordal/Power line: [url]http://www.geogebratube.org/material/show/id/33923[/url] [b]→3) Solution[/b] 4) Vector Reduction: [url]http://www.geogebratube.org/material/show/id/33963[/url] Power Center tool: [url]http://www.geogebratube.org/material/show/id/55255[/url]