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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 first Morley center is the center of Morley's circle. It has triangle center function alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C) and is Kimberling center X_(356).

The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...

The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

The second Napoleon point N^', also called the inner Napoleon point, is the concurrence of lines drawn between polygon vertices of a given triangle DeltaABC and the opposite ...

The MacBeath inconic of a triangle is the inconic with parameters x:y:z=a^2cosA:b^2cosB:c^2cosC. (1) Its foci are the circumcenter O and the orthocenter H, giving the center ...

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 ...

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 ...