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The Tixier point X_(476) is the reflection of the focus of the Kiepert parabola (X_(110)) in the Euler line. It has equivalent trilinear center functions X_(476) = ...

The sum of the angles of a triangle is two right angles. This postulate is equivalent to the parallel postulate.

The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

Given a reference triangle DeltaABC, the trilinear vertex matrix of another triangle DeltaA^'B^'C^' is the 3×3 matrix whose rows are the trilinear coordinates of the vertices ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

The Tucker-Brocard cubic is the triangle cubic with trilinear equation abcsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2)=alphabetagammasum_(cyclic)a^2(b^4+c^4). It passes through ...

The Tucker cubic is the triangle cubic with trilinear equation secAsecBsecCsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2) =alphabetagammasum_(cyclic)asecA(b^2sec^2B+c^2sec^2C). It ...

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

One name for the figure used by Euclid to prove the Pythagorean theorem.

The Yff central circle, a term coined here for the first time, is the circumcircle of the Yff central triangle.