Arc Lengths By the end of today, you will know about arcs and their measures and be able to do operations involving them.

Arc Length Arc length is a part of the circumference of a circle and is found by using a proportion. arc length = arc measure circumference 360

Example In Circle P, find the length of arc AB

Central Angle Measure of an Arc Length of an Arc A central angle of a circle is an angle whose vertex is the center of the circle. When we say the measure of an arc, we are referring to the degree measure. When we say the length of the arc, we are referring to the portion of the circumference the arc covers. Measure of an Arc Length of an Arc

Notation When naming an arc, for instance arc AB, we use the notation When talking about the degree measure of an arc, we use the notation

Minor Arc The measure of a minor arc is the measure of its central angle. The measure of the entire circle is 360o. The measure of a major arc is the difference between 360o and the measure of the related minor arc. Major Arc

Semicircle A semicircle is an arc the endpoints that are the endpoints of a diameter.

Arc Addition Postulate The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs

Find the measure of each indicated arc below for circle P shown

Congruent Circles Congruent Arcs Two circles are congruent circles if they have the same radius. Two arcs are congruent arcs if the have the same measure and they are arcs of the same circle or of congruent circles. Congruent Arcs

Tell whether the red arcs are congruent.

Assignment P. 661 #1-17, 21, 25(a)