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The symmedial circle is the circumcircle of the symmedial triangle. It has circle function l=(bc(a^4-a^2b^2-b^4-a^2c^2-b^2c^2-c^4))/(2(a^2+b^2)(a^2+c^2)(b^2+c^2)), (1) which ...
The tangential mid-arc circle is the circumcircle of the tangential mid-arc triangle. Its center and radius appear to be very complicated functions. Its center is not in ...
The third Lemoine circle, a term coined here for the first time, is the circumcircle of the Lemoine triangle. It has center function alpha=(f(a,b,c))/a, (1) where f(a,b,c) is ...
The third mid-arc point is the triangle center with triangle center function alpha_(2089)=[-cos(1/2A)+cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(2089).
The third Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 357, 358, 1136, and 1137.
The third power point is the triangle center with triangle center function alpha_(32)=a^3. It is Kimberling center X_(32).
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 ...
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