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Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...

The point of coincidence of P and P^' in Fagnano's theorem.

The point of concurrence of the joins of the vertices of a triangle and the points of contact of an inconic of the triangle (Veblen and Young 1938, p. 111; Eddy and Fritsch ...

The extangents triangle is homothetic to the orthic triangle, and its homothetic center is known as the Clawson point, or sometimes the "crucial point." It has equivalent ...

The Euler infinity point is the intersection of the Euler line and line at infinity. Since it lies on the line at infinity, it is a point at infinity. It has triangle center ...

The point F at which the incircle and nine-point circle are tangent. It has triangle center function alpha=1-cos(B-C) (1) and is Kimberling center X_(11). If F is the ...

p is an equireciprocal point if, for every chord [x,y] of a curve C, p satisfies |x-p|^(-1)+|y-p|^(-1)=c for some constant c. The foci of an ellipse are equichordal points.

The first Napoleon point N, also called the outer Napoleon point, is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of ...