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A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

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 ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

The extouch triangle DeltaT_1T_2T_3 is the triangle formed by the points of tangency of a triangle DeltaA_1A_2A_3 with its excircles J_1, J_2, and J_3. The points T_1, T_2, ...

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 ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

Given a triangle DeltaABC and a point P not a vertex of DeltaABC, define the A^'-vertex of the circumcevian triangle as the point other than A in which the line AP meets the ...