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If the trilinear polars of the polygon vertices of a triangle are distinct from the respectively opposite sides, they meet the sides in three collinear points.

There exists a triangulation point Y for which the triangles BYC, CYA, and AYB have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. For a triangle with side lengths a, b, ...

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...

The golden gnomon is the obtuse isosceles triangle whose ratio of side to base lengths is given by 1/phi=phi-1, where phi is the golden ratio. Such a triangle has angles of ...

"The" Griffiths point Gr is the fixed point in Griffiths' theorem. Given four points on a circle and a line through the center of the circle, the four corresponding Griffiths ...

Let A^' be the outermost vertex of the regular pentagon erected inwards on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The inner Soddy circle is the circle tangent to each of the three mutually tangent circles centered at the vertices of a reference triangle. It has circle function ...

Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...