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High Quality Content by WIKIPEDIA articles! In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga posed and solved this famous problem in his work ??????; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them and each solution circle encloses or excludes the three given circles in a different way.In the 16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution does not use only straightedge and compass constructions. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius or expanded to infinite radius. ... Read more

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High Quality Content by WIKIPEDIA articles! n Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (ca. 262 BC ? ca. 190 BC) posed and solved this famous problem in his work ?????? (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2) and each solution circle encloses or excludes the three given circles in a different way. ... Read more