10-6 Circles and Arcs

Essential Understanding

You can find the length of part of a circle’s circumferences by relating it to an angle in the circle

Students will be able to find the measures of central angles and arcs

Students will be able to find the circumference and arc length

Vocabulary

Circle: set of all points equidistant from a given point called the center Named by its center. Ex. Circle P (P)

Diameter: segment that contains the center and ahs both endpoints on the circle

Radius: segment that has one endpoint at the center and the other endpoint on the circle

Congruent circles: have congruent radii

Central Angle: an angle whose vertex is the center of the circle

Parts of a Circle

Arcs

Semicircle: type of arc called that is half of a circle Named by its endpoints and another point on

the arc

Minor Arc: smaller than a semicircle Named by its endpoints

Major Arc: larger than a semicircle Named by its endpoints and another point on

the arc

Naming Arcs

What are the minor arcs of A?

What are the semicircle of A?

What are the major arcs of A that contain point Q?

Arc Addition Postulate

The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Arc ABC = arc AB + arc BC

Finding the Measures of Arcs

Circumference of a Circle

Distance around the circle

C = πd or C = 2πr

All circles are similar to each other, therefore a similarity transformation can be done that maps any circle to another circle

Concentric circles: coplanar circles that have the same center

Finding a Distance

A car has a circular turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. How much farther does a tire on the outside of the turn travel than a tire on the inside?

Finding a Distance

A merry-go-around has seats 7 feet from the center of the ride and 10 feet from the center. How much further does a child seated on the outside loop travel than a child seated on the inside loop in one complete revolution?

Arc Length

Distance of a fraction of the circumference

The length of an arc of a circle is the product of the ratio (measure of the arc) and the circumference of the circle. 360

Finding Arc Length in Red

Finding Arch Length

What is the length of a semicircle with radius 1.3m? Leave your answer in terms of π.

Homework

Pg. 654

#9 – 11, 12 – 27 (3s), 28 – 32, 43

15 problems