Quandaries
and Queries
Name: Mitja
Who is asking: Student
Level: Secondary
Question:
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."
Chris