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Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

The first Brocard point is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...

The geometric centroid of a quadrilateral lamina is the center of its Wittenbauer's parallelogram.

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...

The Lucas cubic is a pivotal isotomic cubic having pivot point at Kimberling center X_(69), the isogonal conjugate of the orthocenter, i.e., the locus of points P such that ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...

The Yiu A-circle of a reference triangle DeltaABC is the circle passing through vertex A and the reflections of vertices B and C with respect to the opposite sides. The Yiu ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...

Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

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 ...