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The third Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 357, 358, 1136, and 1137.

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

The Steiner circumellipse is the circumellipse that is the isotomic conjugate of the line at infinity and the isogonal conjugate of the Lemoine axis. It has circumconic ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

The Euler triangle formula states that the distance d between the incenter and circumcenter of a triangle is given by d^2=R(R-2r), where R is the circumradius and r is the ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

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 ...

Trigonometry

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...