This construction of an orthogonal circle is useful in understanding the radical axis of two circles, and the inverse of "'P "'with respect to the given circle.
2.
Power with respect to both given circles, because the tangents from "'P "'( blue lines ) are radii of the orthogonal circle and thus have equal length . ]]
3.
If the radical center lies outside of all three circles, then it is the center of the unique circle ( the "'radical circle "') that intersects the three given circles orthogonally; the construction of this orthogonal circle corresponds to "'Monge's problem " '.
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