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The Stammler triangle is the triangle formed by the centers of the Stammler circles. It is an equilateral triangle. It circumscribes the circumcircle and homothetic to the ...

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

The Malfatti triangle DeltaGamma_AGamma_BGamma_C of a reference triangle DeltaABC is the triangle formed by the centers of its Malfatti circles.

The third Brocard triangle is Gibert's term for the isogonal conjugate of the first Brocard triangle. It has trilinear vertex matrix [b^2c^2 ab^3 ac^3; a^3b a^2c^2 bc^3; a^3c ...

A triangle DeltaA^'B^'C^' is said to be circumscribed in a triangle DeltaABC if A lies on B^'C^', B lies on C^'A^', and C lies on A^'B^' (Kimberling 1998, p. 185). Examples ...

A drafter triangle is a name sometimes used to refer to a 30-60-90 triangle. For this reason, a polyform consisting of multiple 30-60-90 triangles is known as a polydrafter.

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 ...

The triangle DeltaA^'B^'C^' formed by the points of pairwise intersection of the three intangents. It is not in perspective with DeltaABC. It has trilinear vertex matrix ...

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 ...