Circles: Special Segments in Circles

Circle

Before we begin studying special segments in a circle, let’s define a circle.

A circle is made up of all the points that are equidistant from a center point.


Take a look at the following points.

Points that are all equidistance from a center point.
Points equidistant from a Center Point


Notice that all the points around the outside are the same distance from the center.  If we continued to draw more and more points it would eventually make a complete circle.
 

Radius of a Circle

The radius (plural is radii) of a circle is the distance from the center point to a point on the circle. We also use the term radius to refer to any line segment drawn from the center to any point on a circle.


In the following circle, the center is point P.  We call this Circle P, or Circle P.  Segment PQ is a radius of the circle and the radius equals 5 centimeters.

circle with center P and point Q on circle, line segment from P to Q is drawn and labeled 5 centimeters
Circle P

Diameter of a Circle

If a radius is extended past the center to a point on the other side of the circle, it is called the diameter.

The diameter of a circle is the distance from one point on the circle, through the center, to another point on the circle.  We also use the term diameter to refer to any line segment drawn from one point on the circle, through the center, to another point on the circle.


In the following circle, the center is point C.  We call this Circle C, or Circle C.  Segment XY is a diameter of the circle and the diameter equals 14 inches.

circle with center C and points X and Y on circle, line segment from X to Y is drawn through point C and labeled 14 inches.
Circle C