AMSCO'S Geometry. New York - Rye High School

538 Geometry of the CircleF8080GOEIn circle O, GOE is a straight angle, mGOE 180, and mFOG 80.Therefore, the degree measure of FG X is 80°, written as mFGX 5 80 . Also, sincemGFE X 5 180 ,mFE X 5 180 2 80mFEG X 5 100 1 180andTherefore,5 1005 280mGFX 1 mFEG X 5 80 1 2805 3601. The degree measure of a semicircle is 180. Thus:2. The degree measure of a major arc is equal to 360 minus the degree measureof the minor arc having the same endpoints.Do not confuse the degree measureAof an arc with the length of anarc. The degree measure of every circleAis 360 but the circumference of acircle is 2p times the radius of the circle.Example: in circle O, OA 1 cm,and in circle O, OA 1.5 cm. InOOboth circles, the degree measure of the circle is 360° but the circumference ofcircle O is 2p centimeters, and the circumference of circle O is 3p centimeters.Congruent Circles, Congruent Arcs,and Arc AdditionDEFINITIONCongruent circles are circles with congruent radii.IfOC > OrCr, then circles O and O are congruent.CCOODEFINITIONCongruent arcs are arcs of the same circle or of congruent circles that are equalin measure.