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The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle. Its trilinear vertex matrix is ...

The second Brocard Cevian triangle is the Cevian triangle of the second Brocard point. It has area Delta_2=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

The second Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-2pi)] sec[1/3(B-2pi)]; sec[1/3(C-2pi)] 2 sec[1/3(A-2pi)]; sec[1/3(B-2pi)] sec[1/3(A-2pi)] 2]. The ...

The third Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-4pi)] sec[1/3(B-4pi)]; sec[1/3(C-4pi)] 2 sec[1/3(A-4pi)]; sec[1/3(B-4pi)] sec[1/3(A-4pi)] 2]. The ...

The tangential mid-arc triangle of a reference triangle DeltaABC is the triangle DeltaA^'B^'C^' whose sides are the tangents to the incircle at the intersections of the ...

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The equilateral cevian triangle point of a triangle is the unique point P such that the Cevian triangle of P is equilateral. This point is Kimberling center X_(370).

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

Given an original triangle (thick line), find the medial triangle (outer thin line) and its incircle. Take the pedal triangle (inner thin line) of the medial triangle with ...