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Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

An exmedian is a parallel to a side of a triangle through the opposite vertex. So in the above diagram, A_2^'A_3^' is the exmedian of side A_2A_3, and so on. The pairwise ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

Given a reference triangle DeltaABC, the trilinear vertex matrix of another triangle DeltaA^'B^'C^' is the 3×3 matrix whose rows are the trilinear coordinates of the vertices ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...