三個給定圓的八個阿波羅尼斯圓中的任何一個都與一個圓 
相切，該圓被稱為 Hart 圓。另外三個阿波羅尼斯圓也如此，它們與給定圓中的兩個具有 (1) 相似的相切關係，而與第三個具有 (2) 相異的相切關係。
Hart 定理
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阿波羅尼斯圓, Hart 圓使用 探索
參考文獻
Casey, J. "On the Equations and Properties--(1) of the System of Circles Touching Three Circles in a Plane; (2) of the System of Spheres Touching Four Spheres in Space; (3) of the System of Circles Touching Three Circles on a Sphere; (4) of the System of Conics Inscribed to a Conic, and Touching Three Inscribed Conics in a Plane." Proc. Roy. Irish Acad. 9, 396-423, 1864-1866.Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 106-107, 1888.Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, p. 43, 1971.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 127-128, 1929.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 254-257, 1893.Larmor, A. "Contacts of Systems of Circles." Proc. London Math. Soc. 23, 136-157, 1891.在 上被引用
Hart 定理請引用為
Weisstein, Eric W. “Hart 定理。” 來自 ——Wolfram 網路資源。 https://mathworld.tw/HartsTheorem.html