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The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B = sqrt(1-4sin^2omega)R (1) = (2) where R is the ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. Its triangle center function is alpha_(357)=sec(1/3A), which ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

A self-isogonal cubic us a triangle cubic that is invariant under isogonal conjugation. The term is commonly applied to mean a pivotal isogonal cubic, in which points P lying ...

A self-isotomic cubic us a triangle cubic that is invariant under isotomic conjugation. The term is commonly applied to mean a pivotal isotomic cubic, in which points P lying ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

The Simson cubic is the triangle cubic that is the locus of tripoles of the Simson lines of a triangle DeltaABC. It has trilinear equation ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...