Definition: A circle is the set of all points in a plane that are equidistant froma given point called the center of the circle. We use the symbol   to REPRESENTA circle.The a line segment from the center of the circle to any point on the circle is aradius of the circle. By definition of a circle, all RADII have the same length. Wealso 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 givenradius. For example, we can say circle O with radius r.OrThe 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 circleand has the center of the circle as its vertex. In other words, a central anglealways 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 ISA minor arc. An arc that is greater than half a circle is a major arc, and anarc that’s equal to half a circle is a semi-circle.By definition, the degree measure of an arc is the central angle that interceptsthe arc.We use two letters with an arc symbol on top to refer to a minor arc, and threeletters for a major arc.A chord is an line segment that has any two points on the circumference as itsend-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 points.OABECDFFor the circle above, ∠EOB is a central angle. So is ∠DOEDEù is a minor arc. The central angle ∠DOE is the angle that intercepts thisarc. 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 arecongruent 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 congruentAll diameters are congruentA diameter of a circle divides the circle into two equal arcs (semicircles). Conversely, If a chord divides the circle into two equal arcs,then the chord is a diameterCongruent central angles intercept congruent arcs, and conversely, congruent arcs are intercepted by congruent central angles.Congruent chords divide congruent arcs, and conversely, Congruent arcshave congruent chords.DABCE FO O0In the picture above, assume  O ∼=  O0.If central angle ∠AOB ∼= ∠COD ∼= ∠EO0F, thenAB ∼= CD ∼= EF, and ABù ∼= CDù ∼= EFùConversely, if ABù ∼= CDù ∼= EFù, thenAB ∼= CD ∼= EF, and ∠AOB ∼= ∠COD ∼= ∠EO0FLet  O be a circle with center O and radius r, and let P be a point.If the distance between a point P and the center O of a circle is less then theradius of the circle, the point P is inside the circle.If the distance between a point P and the center O of a circle is greater then theradius of the circle, the point is OUTSIDE the circle.If the distance between a point P and the center O of a circle is equal to theradius of the circle, the point is on the circle.ACBOrIn the picture above, C is inside circle  O since OC < r. B is outside circle  OStep-by-step explanation: