The document defines key terms related to circles such as diameter, radius, arcs, and circumference. It explains that the measure of an arc is related to the central angle it intercepts. Students will learn to find the measures of central angles and arc lengths, and how to calculate the circumference of a circle using radius and diameter. Examples are provided for calculating distances traveled along circular paths of different radii.

2. 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

3. 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

4. Parts of a Circle

5. 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

6. 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?

7. 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

8. Finding the Measures of
Arcs

9. 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

10. 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?

11. 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?

12. 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

13. Finding Arc Length in Red

15. Finding Arch Length
 What is the length of a semicircle with radius 1.3m?
Leave your answer in terms of π.

16. Homework
 Pg. 654
 #9 – 11, 12 – 27 (3s), 28 – 32, 43
 15 problems