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The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

The Miquel point is the point of concurrence of the Miquel circles. It is therefore the radical center of these circles. Let the points defining the Miquel circles be ...

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...

A triangle line lalpha+mbeta+ngamma=0 defined relative to a reference triangle is called a central line iff l:m:n is a triangle center (Kimberling 1998, p. 127). If l:m:n is ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

The Bickart points are the foci F_1 and F_2 of the Steiner circumellipse. They have trilinear coordinates alpha_1:beta_1:gamma_1 and alpha_2:beta_2:gamma_2, where alpha_i = ...

Inscribe a triangle in a circle such that the sides of the triangle pass through three given points A, B, and C.