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Abstract
It is well known that there is a unique circle passing through three specified points if and only if they are non-collinear. We show that there is also a unique circle passing through the endpoints of diameters of three specified circles if and only if they have non-collinear centres.
Keywords:
Acknowledgments
The author thanks the anonymous referees for their useful inputs.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 In this note, all circles have positive radius.
2 This at first might call to mind Apollonius' problem of constructing a circle tangent to three specified circles (Dörrie, Citation1965, pp. 154–160). However, such a circle is not unique in general.