Download Circles and Arcs – Section 7

Mrs. Scott
Modern Geometry
Name:___________________________________
Date:____________________________________
7.6 Circles and Arcs
Learning Objectives
1. To find the measure of central angles and arcs.
2. To find circumference and arc length.
In a plane, a _______________________ is the set of all points equidistant from a given point called the
________________. You name a circle by its center.
Picture:
A _________________________ is a segment that has one endpoint at the center and the other endpoint on the
circle. Let’s draw radius PC in the circle above.
______________________________ __________ have congruent radii.
A ________________________________ is a segment that contains the center of a circle and has both
endpoints on the circle. Let’s draw diameter AB in the circle above.
A ____________________ _______________ is an angle whose vertex is the center of the circle. Let’s draw
central angle APC in the circle above.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
An ______________ is part of a circle.
One type of arc, a ___________________________________ is half of a circle.
A ______________________ ___________ is smaller than a semicircle.
A ___________________ ______ is greater than a semicircle.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
______________________________ __________ are arcs of the same circle that have exactly _______
________________ in common!
You can add the measures of adjacent arcs just as you can add the measures of adjacent angles!
7-1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The ________________________________ of a circle is the distance around the circle. The number __ (
is the ratio of the circumference of a circle to its diameter.
7-13
Circles that lie in the same plane and have the same center are ___________________________
_________________________.
)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The measure of an arc is in degrees while the ______ ____________________ is a fraction of a circle’s
circumference.
An arc of 60° represents ___________ or _____________ of the circle. Its arc length is _____ of the
circumference of the circle.
7-13
It is possible for two arcs of different circles to have the same measure but different
lengths as shown. It is possible for arcs of different circles to have the same length
but different measures. ______ _______ are arcs that have the same measure and
are in the same circle OR in congruent circles.
Name _____________________________________ Class _________ Date ________________
Practice 7-6
Circles and Arcs
Find the circumference of each circle. Leave your answers in terms of
1.
In
2.
C,
and
.
3.
are diameters. Identify the following.
4. two major arcs
5. two minor arcs
6. two semicircles
7. a pair of adjacent arcs
8. an acute central angle
9. an obtuse central angle
A market research survey found that adults’ favorite vegetables are as shown below. Find the measure of
the central angle for each of the following vegetables. Give your answers to the nearest degree.
10. potatoes
11. green beans
12. corn
13. carrots
14. broccoli
Find the measure of each arc in
C.
15.
16.
17.
18.
19.
20.
Find the length of each arc. Leave your answers in terms of
21.
22.
.
23.