Circles and Arcs

General Vocabulary: CIRCLE: the set of all points equidistant from a given point called the CENTER RADIUS: a segment that has one point at the center and the other endpoint on the circle DIAMETER: a segment that contains the center of a circle and has both endpoints on the circle

Central Angles CENTRAL ANGLE: an angle whose vertex is on the center of the circle Name all the central angles above. A B C D O

Arcs ARC: part of a circle SEMICIRCLE: half of a circle MINOR ARC: smaller than a semicircle MAJOR ARC: bigger than a semicircle ADJACENT ARCS: arcs of the same circle that have exactly one point in common

Arcs Name all the semicircles above. Name all the minor arcs above. Name all the major arcs that contain point A. D A C E O

Adjacent Arcs Adjacent arcs are arcs of the same circle that have exactly one point in common. You can add the measures of adjacent arcs just like you can add the measures of adjacent angles.

Arcs Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. m ABC = m AB + m BC A B C D O

Circumference and Arc Length Circumference of a Circle: 2πr or πd Arc Length: The length of an arc of a circle is the product of the circumference and (degree measure of arc/360) length of AB = m AB * 2πr 360 A B O r

Circumference and Arc Length Arc Length: length of AB = m AB * 2πr 360 Length of AB = 140 * 2π5 360 Length of AB = A B O C D 5

Circumference and Arc Length Arc Length: length of AB = m AB * 2πr 360 Length of AB = A B O 50 0 C D 12

Misc Congruent circles have congruent radii Concentric circles lie in the same plane and have the same center Congruent arcs have the same measure AND are in the same circle or congruent circles