Quandaries and Queries


Name: Mitja

Who is asking: Student
Level: Secondary

There are given 2 circles lieing one out of another and one point out of both circles. How to construct a circle passing through a given point and internally tangent to one and externally tangent to the other cirlce?



Hi Mitja,

If you know about inversions, then the problem is easy: invert the given circles into a pair of concentric circles. Without inversion, one needs to know many facts about Euclidean constructions -- more than is generally taught in high school. A complete solution is given in many college geometry books under the heading "the problem of Apollonius."



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