Concurrent lines

In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.

The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil. In any affine space (including a Euclidean space) the set of lines parallel to a given line (sharing the same orientation) is also called a pencil, and the vertex of each pencil of parallel lines is a distinct point at infinity; including these points results in a projective space in which every pair of lines has an intersection.