ARCS AND CHORDS Geometry CP1 (Holt 12-2) K.Santos

Central Angle Central angle----an angle whose vertex is the center of a circle. A B O < AOB is a central angle

Chords and Arcs

Arcs and their measures

Arcs

Adjacent Arcs

Arc Addition Postulate

Example

Theorem Within a circle or in congruent circles: (1) Congruent central angles have congruent chords (2) Congruent chords have congruent arcs (3) Congruent arcs have congruent central angles

Example

Theorem

Theorem

Example Find the value of x. 5 x 5 6 Chords are equidistant from the center so the chords are congruent Bottom chord is 2(6) = 12, so the chord on the right is also 12. Thus, x = 12

Example