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The contact triangle of a triangle DeltaABC, also called the intouch triangle, is the triangle DeltaC_AC_BC_C formed by the points of tangency of the incircle of DeltaABC ...

The point F at which the incircle and nine-point circle are tangent. It has triangle center function alpha=1-cos(B-C) (1) and is Kimberling center X_(11). If F is the ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the ...

There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

The BCI triangle DeltaA^'B^'C^' of a triangle DeltaABC with incenter I is defined by letting A^' be the center of the incircle of DeltaBCI, and similarly defining B^' and ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

The circumcircle of the Cevian triangle DeltaA^'B^'C^' of a given triangle DeltaABC with respect to a point P. The following table summarizes a number of named Cevian circles ...