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Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

The Dou circle is the circle cutting the sidelines of the reference triangle DeltaABC at A^', A^(''), B^', B^(''), C^', and C^('') such that ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

The intangents circle is the circumcircle of the intangents triangle. It has circle function l=((-a+b+c)f(a,b,c))/(8a^2b^2c^2cosAcosBcosC), (1) where (2) which is not a ...

The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...

The anticomplementary circle is the circumcircle of the anticomplementary triangle. It has radius R_A=2R, where R is the circumradius of the reference triangle, and center at ...

In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is a(x_1^2+x_2^2)+2fx_2x_3+2gx_1x_3+cx_3^2=0. The discriminant of this circle is defined as Delta=|a 0 g; ...