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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 Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...

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 circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

Synergetics coordinates are a set of triangular coordinates in their plane (or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions). ...

A symbol consisting of three rational numbers that can be used to describe uniform polyhedra based on how a point C in a spherical triangle can be selected so as to trace the ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...