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Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

The Jerabek center X_(125) (center of the Jerabek hyperbola) lies on the nine-point circle. The Jerabek antipode is the antipode of this point on nine-point circle. It has ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

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 ...

A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the ...

Lemoine geometry is that part of triangle geometry concerned with symmedians and symmedian points.

If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

The Lucas central circle is the circumcircle of the Lucas central triangle. The center, radius, and circle function appear to be complicated, and neither the center nor the ...