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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).

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

The Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble ...

A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the ...

Lemoine-Brocard geometry is that part of triangle geometry concerned with the Brocard points, Brocard triangles, etc. and with symmedians and symmedian points.

Lemoine geometry is that part of triangle geometry concerned with symmedians and symmedian points.

A point that lies on one of the sides of a triangle but is a not vertex.

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).

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...