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The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

A zero vector, denoted 0, is a vector of length 0, and thus has all components equal to zero. It is the additive identity of the additive group of vectors.

The letter O is used for a number of different purposes in mathematics. The double-struck O is sometimes used to represent octonions. The symbols O(x) (sometimes called the ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

The Bevan point V of a triangle DeltaABC is the circumcenter of the excentral triangle DeltaJ_AJ_BJ_C. It is named in honor of Benjamin Bevan, a relatively unknown Englishman ...

A bicentric quadrilateral, also called a cyclic-inscriptable quadrilateral, is a four-sided bicentric polygon. The inradius r, circumradius R, and offset x are connected by ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

Given a point P and a triangle DeltaABC, the Cevian triangle DeltaA^'B^'C^' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A ...