Geometry

A circle is a set of points in a plane which are a fixed distance from a point called the center, C (see Figure 4). A "chord" is a segment, DE, joining two points on the circle; a radius is segment, CA, joining the center and a point on the circle; a diameter is a chord, DB, through the center. A "tangent," DF, is a line touching the circle in a single point. The words "radius" and "diameter" can also refer to the lengths of these segments.

An "arc" is the portion of the circle between two points on the circle, including the points. A major arc is the longer of the two arcs so determined; a minor arc, the shorter. When an arc is named it is usually the minor arc that is meant, but when there is danger of confusion, a third letter can be used, e. g. arc DAB.

All circles are similar, and because of this the ratio of the circumference to the diameter is the same for all circles. This ratio, called pi or π, was shown to be smaller than 22/7 and larger than 223/71 by the mathematician Archimedes about 240 B.C.

An arc can be measured by its length or by the central angle which it subtends. A central angle is one whose vertex is the center of the circle.

An inscribed angle is one whose vertex is on the circle and whose sides are two chords or one chord and a tangent. Angles EDB and BDF are inscribed angles. The measure of an inscribed angle is one half that of its intercepted arc. Any inscribed angle that intercepts a semicircle is a right angle; so is the angle between a tangent and a radius drawn to the point of tangency.

If X is a point inside a circle and AB and CD any two chords through X, then X divides the chords into segments whose products are equal. That is, AX XB = CX XD.

Figure 5. Illustration by Hans & Cassidy. Courtesy of Gale Group.