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For triangles in the plane, AD·BE·CF=BD·CE·AF. (1) For spherical triangles, sinAD·sinBE·sinCF=sinBD·sinCE·sinAF. (2) This can be generalized to n-gons P=[V_1,...,V_n], where ...

Three sets of three lines such that each line is incident with two from both other sets.

A function f(x) has a vertical tangent line at x_0 if f is continuous at x_0 and lim_(x->x_0)f^'(x)=+/-infty.

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

The excentral triangle, also called the tritangent triangle, of a triangle DeltaABC is the triangle J=DeltaJ_AJ_BJ_C with vertices corresponding to the excenters of DeltaABC. ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

AW, AB, and AY in the above figure are in a harmonic range.