Geometry: Basic Terms

Basic Terms

Start with a point C, and collect all of the points a fixed distance r units away from it. Give this collection of points a name: circle. I have drawn a circle in Figure 17.1. The starting point is called the center of the circle. Any line segment having the center of the circle as one endpoint and any point on the circle as the other endpoint is called a radius of the circle. Because all points on the circle are a distance of r units away from the center, all radii of a circle are congruent. This will be stated as a theorem, though the proof would take no more than a line or two, with the reasons being either “given” or “definition of a circle.”

Figure 17.1A circle with center C and radius ¯AC.

• Theorem 17.1: All radii of a circle are congruent.

Don't limit yourself to only drawing radii of circles. Circles get really interesting when you connect points on a circle. A line segment that joins two points on the circle is called a chord of the circle. A diameter of a circle is a chord that contains the center of the circle. The length of a diameter of a circle is twice the length of the radius of a circle. This can be proven by using the Segment Addition Postulate (Postulate 3.5).

If you have three points on a circle, you can connect them to form an inscribed angle. An inscribed angle of a circle is an angle whose vertex is a point on the circle and whose sides are chords of the circle. You can also construct inscribed polygons by using points on the circle as the vertices.

Two circles that coincide are congruent. In order for two circles to be congruent, the lengths of the radii must be congruent. If two circles have the same center they are called concentric circles.

There are times when you will need to measure the distance around the circle. When you did this with polygons, it was called the perimeter. With circles, it will be called the circumference of the circle.