10.6: Circles and Arcs

A circle is all points equidistant from a given point, called the center. The diameter of the circle is a line segment that contains the center of the circle and has endpoints on the edge of the circle. The radius is a line segment from the center to the edge of the circle. If two circles are congruent, they have congruent radii. A central angle is an angle whose vertex is the center of the circle.

An arc is some portion of a circle An arc is some portion of a circle. A semicircle is exactly half a circle. A major arc is larger than a semicircle, and a minor arc is smaller. A minor arc is referred to by its endpoints, and a major arc(or semicircle) is referred to by its endpoints plus another point. Adjacent Arcs are arcs of the same circle that share exactly one point

What are the minor arcs of this circle? What are the major arcs containing point A? What are the semicircles you can form?

What is the measure of each arc? BC CD BCD DA AB

What is the measure of each arc? PRS RS PQ QPR

Circles that share the same center are known as concentric circles

Arc length is different from the measure of an arc Arc length is different from the measure of an arc. The measure of an arc is related to the central angle, whereas arc length is a fraction of the circumference.

Is Arc length (like we previously calculated) proportional to the radius? A radian is a measurement similar to degrees. It is defined as the ratio between arc length and radius, where 1 radian = the central angle of a circle such that its arc measure is equal to the radius of the circle Radian Measure = arc length / radius

Homework Section 10.6, pages 654-655: 9, 10, 12, 15, 18, 21, 24, 25, 30, 33 Honors: Add 29, 43