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 • 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 centralangle. • 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
Congruent Circles • 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
Assignment • p.661: 3-14 • p.751: 15-23