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Two curves are tangent externally at a point P if they lie on opposite sides of their common tangent at P

Two curves are tangent internally at a point P if they lie on the same side of their common tangent at P

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

An N-cluster is a point lattice configuration in which the distance between every pair of points is an integer, no three points are collinear, and no four points are ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

The isotomic conjugate of a point is the point of concurrence Q of the isotomic lines relative to a point P. The isotomic conjugate alpha^':beta^':gamma^' of a point with ...

The trilinear pole of the orthotransversal of a point P is called its orthocorrespondent. The orthocorrespondent of a point P=p:q:r is given by where S_A, S_B, and S_C is ...

If two perpendicular lines are drawn through the orthocenter H of any triangle, these lines intercept each side (or its extension) in two points (labeled P_(12), P_(12)^', ...