Definition: A circle is the set of all points in a PLANE that are equidistant from a given point called the center of the circle. We use the symbol to represent a circle. The a LINE segment from the center of the circle to any point on the circle is a radius of the circle. By definition of a circle, all radii have the same length. We also use the term radius to mean the length of a radius of the circle. To refer to a circle, we may refer to the circle with a given center and a given radius. For EXAMPLE, we can say circle O with radius r. O r The circumference of a circle is the length around the circle. A central angle of a circle is an angle that is formed by two radii of the circle and has the center of the circle as its vertex. In other words, a central angle always has its vertex as the center of the circle. An arc is a connected portion of a circle. An arc that is less than half a circle is a minor arc. An arc that is greater than half a circle is a major arc, and an arc that’s equal to half a circle is a semi-circle. By definition, the degree measure of an arc is the central angle that intercepts the arc. We use two letters with an arc symbol on top to refer to a minor arc, and three letters for a major arc. A chord is an line segment that has any two points on the circumference as its end-points. A chord always lies inside a circle. A diameter of a circle is a chord that contains the center of the circle. A secant is a line that intersects the circle at two pointsStep-by-step explanation:For the circle above, ∠EOB is a central angle. So is ∠DOE DEù is a minor arc. The central angle ∠DOE is the angle that intercepts this arc. The (degree) measure of DEù is the measure of ∠DOE. DCB üis a major arc. CBù is a semi-circle. CB is a diameter. DE is a chord. F A is a secant. By definition, two circles are congruent if their radii are congruent. Two arcs are congruent if they have the same degree measure and same length. Postulates and/or facts: For circles that are congruent or the same: All radii are congruent All diameters are congruent A diameter of a circle divides the circle into two equal arcs (semi- circles). Conversely, If a chord divides the circle into two equal arcs, then the chord is a diameter Congruent central angles INTERCEPT congruent arcs, and conversely, con- gruent arcs are intercepted by congruent central angles. Congruent chords divide congruent arcs, and conversely, Congruent arcs have congruent chords.