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The Kiepert center is the center of the Kiepert hyperbola. It is Kimberling center X_(115), which has equivalent triangle center functions alpha_(115) = ((b^2-c^2)^2)/a (1) ...

Given the "peaks" of three equilateral triangles placed on the sides of a triangle T, construct T. The problem was proposed by Lemoine (1868) and solved for the general case ...

Also known as the a Lorentz transformation or Procrustian stretch, a hyperbolic transformation leaves each branch of the hyperbola x^'y^'=xy invariant and transforms circles ...

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 ...

The Kiepert center X_(115) (center of the Kiepert hyperbola) lies on the nine-point circle. The Kiepert antipode is the antipode of this point on nine-point circle. It has ...

The Jerabek center is the center of the Jerabek hyperbola. It is Kimberling center X_(125), which has equivalent triangle center functions alpha_(125) = cosAsin^2(B-C) (1) ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...

For a unit circle with parametric equations x = cost (1) y = sint, (2) the negative pedal curve with respect to the pedal point (r,0) is x_n = (r-cost)/(rcost-1) (3) y_n = ...

For a given curve C, consider the locus of the point P from where the tangents from P to C meet at a fixed given angle. This is called an isoptic curve of the given curve. ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...