A circle is the set of all points that are equidistant from and in the same plane as a point called the center.  The center is not a part of the circle but helps define it.  Since all the points on the circle are the same distance from the center, we can use that to create segments of equal length.  We do that by dividing the circle into parts.  These parts are called arcs.  No arc is straight.

A regular triangle can be created by dividing a circle into 3 congruent arcs.  Since the circle is divided into 360º, each arc will be 120º.  In a circle, congruent arcs cut off congruent chords.  These chords are segments that form a triangle.  A convex polygon that has all its vertices on the circle is inscribed in the circle.

There two kinds of angles that are associated with inscribing polygons.  One is a central angle.  A central angle has its vertex at the center of the circle.  The central angle has the same measure of the arc it cuts off.  On the left angle CBD and minor arc CD are both 120 º.

Another kind of angle is an inscribed angle.  An inscribed angle has its vertex on the circle.  The measure of an inscribed angle is half the measure of its intercepted arc.