Geodesic
A Conformal Proof of a Jordan Curve Problem
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 673-674

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The following theorem appears in [1].Let R be a closed simply connected region of the inversive plane bounded by a Jordan curve J, and let J be divided into three closed arcs A1, A2, A3. Then there exists a circle contained in R and having points in common with all three arcs. 
Spoar, G.; Lane, N.D. A Conformal Proof of a Jordan Curve Problem. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 673-674. doi: 10.4153/CMB-1969-087-8
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     author = {Spoar, G. and Lane, N.D.},
     title = {A {Conformal} {Proof} of a {Jordan} {Curve} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {673--674},
     year = {1969},
     volume = {12},
     number = {5},
     doi = {10.4153/CMB-1969-087-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-087-8/}
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