pencil

A pencil is a set of geometric objects, usually either congruent orsimilar to each other, that share a common incidence property. Below are some of the most commonly encountered pencils:

1. A pencil of lines usually means a set of straight lines that are incident with one point. If the lines all lie in the same plane, the pencil is sometimes called a flat pencil.

2. In some cases, a pencil of lines denotes a set of parallel lines in a plane. If a point of infinity is added to the plane, then we are back to the previous example.

3. A pencil of circles can mean that either these circles all intersect at exactly one point (or share the same tangent line)

4. A pencil of circles can also mean that the circles have two common points of intersection.