Hart Circle Picture created with Autocad

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 circle In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incente ...

s 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 Sir Andrew Searle Hart (1811–1890) was an Anglo-Irish mathematician and Vice-Provost of Trinity College Dublin (TCD). Early life and background He was the youngest son of the Rev. George Vaughan Hart of Glenalla, County Donegal, and his wife ...

. They can be seen as analogous to the

nine-point circle In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: * The midpoint of each s ...

of straight-sided triangles.

References

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External links

History of the Nine-Point Circle, Cambridge University

Discussion of Hart Circle in context of Feuerbach's theorem

On Centers and Central Lines of Triangles in the Elliptic Plane

CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein
Geometry Triangles Circles Triangle geometry Polygons Eponymous geometric shapes