Introduction: A circle is all points equidistant from one point called the center of the circle. Segments drawn near and through the circle create other geometrical objects which we define.

The Lesson:

We show circle O below. A circle is named based on the name of the point which is the center. The segment OA is a radius of the circle.

Definition: A radius is the segment connecting (sometimes referred to as the “distance between”) the center and the circle itself.

In the diagram below, we show circle O with radius OA.

Segments and lines of interest are:

• QA: this is a chord
• RA: this is a chord and it is also a diameter of circle O
• AP: this is a tangent to the circle
• Line AR is called a secant

Definitions:

• diameter: the segment connecting two points of the circle and containing the center
• chord: any segment with endpoints on the circle
• tangent: any segment, which if extended in either direction, will only intersect the circle once
• secant: a segment or line which passes through a circle, intersecting at two points

In the diagram below, we show circle O.

Angles of interest are:

• angle AOP: this is a central angle
• angle RAP: this is an inscribed angle
• angle QAP: this is also an inscribed angle

Definitions:

• A central angle is an angle in a circle with vertex at the center of the circle
• An inscribed angle is an angle formed by three points on a circle