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Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

The first mid-arc point is the triangle center with triangle center function alpha_(177)=[cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(177).

The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

The larger an arc is, the smaller its radius appears. For example, the three arcs illustrated above belong circles of the same radius.

There are two different definitions of the mid-arc points. The mid-arc points M_(AB), M_(AC), and M_(BC) of a triangle DeltaABC as defined by Johnson (1929) are the points on ...

The tangential mid-arc circle is the circumcircle of the tangential mid-arc triangle. Its center and radius appear to be very complicated functions. Its center is not in ...

The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle. Its trilinear vertex matrix is ...

The first mid-arc point is the triangle center with triangle center function alpha_(178)=[cos(1/2B)+cos(1/2C)]csc(1/2A). It is Kimberling center X_(178).

The third mid-arc point is the triangle center with triangle center function alpha_(2089)=[-cos(1/2A)+cos(1/2B)+cos(1/2C)]sec(1/2A). It is Kimberling center X_(2089).

The tangential mid-arc triangle of a reference triangle DeltaABC is the triangle DeltaA^'B^'C^' whose sides are the tangents to the incircle at the intersections of the ...