Hart circle
File:Hart Circle Picture created with Autocad.png
In geometry, the Hart circle is derived from three given circles that cross pairwise to form eight circular triangles. For any one of these eight triangles, and its three neighboring triangles, there exists a Hart circle, tangent to the inscribed circles of these four circular triangles. Thus, the three given circles have eight Hart circles associated with them. The Hart circles are named after their discover, Andrew Searle Hart. They can be seen as analogous to the nine-point circle of straight-sided triangles.{{Cite book |last=Coolidge |first=Julian Lowell |url=https://www.worldcat.org/oclc/1017317 |title=A treatise on the circle and sphere |date=1916 |publisher=Clarendon Press |isbn=0-8284-0236-1 |location=Oxford |oclc=1017317}}{{mathworld|title=Hart Circle|id=HartCircle}}
References
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External links
- [https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F35C6273A2DC54CE806063838A3CB3A0/S0013091500031163a.pdf/div-class-title-history-of-the-nine-point-circle-div.pdf History of the Nine-Point Circle, Cambridge University]
- [https://www.cut-the-knot.org/Curriculum/Geometry/HartCircle.shtml Discussion of Hart Circle in context of Feuerbach's theorem]
- [https://www.researchgate.net/publication/317000577_On_Centers_and_Central_Lines_of_Triangles_in_the_Elliptic_Plane On Centers and Central Lines of Triangles in the Elliptic Plane]
- [https://books.google.com/books?id=D_XKBQAAQBAJ&dq=hart+circle+triangle&pg=PA1311 CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein]