The set of all points that are equidistant is the circle with the given point at the center of the circle. The Radius is a segment with endpoints at the center and on the circle. Next segment is the chord that has both endpoints on the circle, which could also turn into a diameter that passes through the center of the circle. There are two types of line: Secant which intersects the circle in exactly TWO points and Tangent which intersects the circle in exactly ONE point known as the Point of Tangency.

The Central angle is an angle whose vertex is at the center of the circle and the Inscribed Angle is an angle whose vertex is ON the circle. An arc is a portion of the edge of a circle defined by two endpoints. An arc whose measure is less than 180 is a Minor angle while an arc whose measure is greater than 180 is a major. The last arc known as the Semicircle, whose measure is equal to 180 while its endpoints are on the diameter.

An Inscribed Angle is an angle whose vertex is ON the circle and whose sides are chords of the circle. An intercepted arc is an arc formed by an inscribed angle and the measure of that angle is half the measure of its intercepted arc.

Intercepting a Semicircle: If an inscribed angle intercepts a semicircle (diameter), then it is a right angle.

Overlapping Arcs: If two inscribed angles intercept the same arc, then the angles are congruent.

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is half the measure of its intercepted arc.

If two chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of arcs intercepted by the angle and its vertical angle.

If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of the intercepted arcs.