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The line on which the orthocenter H, triangle centroid G, circumcenter O, de Longchamps point L, nine-point center N, and a number of other important triangle centers lie. ...

A transformation characterized by an invariant line and a scale factor (one-way stretch) or two invariant lines and corresponding scale factors (two-way stretch).

A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

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 ...

The Euler-Gergonne-Soddy triangle is the right triangle DeltaZFlEv created by the pairwise intersections of the Euler line L_E, Soddy line L_S, and Gergonne line L_G. (The ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

If the three straight lines joining the corresponding vertices of two triangles ABC and A^'B^'C^' all meet in a point (the perspector), then the three intersections of pairs ...