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 Math Central Quandaries & Queries
 Question from Margaret, a student: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates?

Almost! You would have to be given the centers AND the radii of the three outer circles; even then there might be two circles that are tangent to the three outer circles, in which case you would not be able to determine which was the one you started with. Your problem reduces to the classical problem of Apollonius that deals with finding the circles tangent to three given circles:

http://en.wikipedia.org/wiki/Problem_of_Apollonius

In general there will be eight circles that are tangent to three given circles, but there will be either just one or two of them that could serve as your central circle.

Chris

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.