三个给定圆的八个阿波罗尼斯圆中的任何一个都与一个圆 
相切，该圆被称为 Hart 圆。另外三个阿波罗尼斯圆也如此，它们与给定圆中的两个具有 (1) 相似的相切关系，而与第三个具有 (2) 相异的相切关系。
Hart 定理
另请参阅
阿波罗尼斯圆, Hart 圆使用 Wolfram|Alpha 探索
参考文献
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 Wolfram|Alpha 上被引用
Hart 定理请引用为
Weisstein, Eric W. “Hart 定理。” 来自 MathWorld——Wolfram 网络资源。 https://mathworld.net.cn/HartsTheorem.html