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The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a, (1) which does ...

The Euler points are the midpoints E_A, E_B, E_C of the segments which join the vertices A, B, and C of a triangle DeltaABC and the orthocenter H. They are three of the nine ...

The extangents triangle is homothetic to the orthic triangle, and its homothetic center is known as the Clawson point, or sometimes the "crucial point." It has equivalent ...

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The Gibert point can be defined as follows. Given a reference triangle DeltaABC, reflect the point X_(1157) (which is the inverse point of the Kosnita point in the ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

While the pedal point, Cevian point, and even pedal-Cevian point are commonly used concepts in triangle geometry, there seems to be no established term to describe the ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...