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The geometric centroid of the first Morley triangle, which is also the center of Morley's circle, is called the first Morley center. It has triangle center function ...

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 ...

The triangle center with triangle center function alpha=A.

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 second power point is the triangle center with triangle center function alpha_(31)=a^2. It is Kimberling center X_(31).

The third power point is the triangle center with triangle center function alpha_(32)=a^3. It is Kimberling center X_(32).

The first isodynamic point S has triangle center function alpha_(15)=sin(A+1/3pi) and is Kimberling center X_(15) (Kimberling 1998, p. 68).

The second isodynamic point S^' has triangle center function alpha=sin(A-1/3pi) and is Kimberling center X_(16) (Kimberling 1998, p. 69).

A triangle center is regular iff there is a triangle center function which is a polynomial in Delta, a, b, and c (where Delta is the area of the triangle) such that the ...

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 ...