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Circles and Arcs
Objective:
To find the measure of central angles and arcs.
To find circumference and arc length.
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Good Morning!
AGENDA
HOMEWORK

Homework Check/Quiz Return


Post Right Triangle DDM [19
points]
NONE. (Yes, you read that
correctly.)

Check Aspen and make sure
you are not missing
assignments from previous
absences.

Pre Circle DDM

Notes: Circles and Arcs
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Welcome to Unit 3!
CIRCLES
http://padlet.com/alyssa_gage/circles
WAC Type 1:
List 3 things you
already know
about circles.
1._________
2._________
3._________
+ Circles
A circle is the set of all points
equidistant from a given point
called the center. You name a
circle by its center.
A radius is a segment that
has one endpoint at the
center and the other
endpoint on the circle.
A diameter is a segment
that contains the center of
a circle and has both
endpoints on the circle.
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An arc is a part of the circle.
A central angle is an angle whose vertex
is the center of the circle.
A minor arc is smaller
than a semicircle.
A major arc is greater
than a semicircle.
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Semicircle
One type of arc is a semicircle.
The measure of a
semicircle is 180
degrees. The measure of
a minor arc is the
measure of its
corresponding central
angle.
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Example #1
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Example #2
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Circumference
Find the circumference of each circle. Leave your answer in
terms of
p
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Arc Length
The measure of an arc is in degrees while the arc length
is a fraction of a circle’s circumference.
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Example #3-Finding Arc Length
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Example #4-Finding Arc Length
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Example #5
A
P
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Objective:
Arc Length and
Area of a Sector
To find circumference and arc length.
To find area and the area of a sector.
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TGIF!
Agenda

Warm Up

Whiteboards-Recap from last
time

Notes-Arc Length/Area Sector
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Friday Friends Practice
Homework

Arc Length and Area of a
Sector Worksheet
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Recall from last class…
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Arc Length Example #1
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Arc Length Example #2
+ The Marshfield Skate Park is thinking of constructing some
new ramps. A “half pipe” ramp is formed by two quarter-circle
ramps, each of which is 10 feet high, plus a flat space 20 feet
long between the centers.
Find the distance a skater travels from the top of one ramp to the top of the other.
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Sectors
Region bounded by an arc of the circle and the
two radii to the arcs endpoints
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Example #3
Finding the Area of a Sector
Find what fraction of the circle is shaded.
Multiply the fraction shaded by the
entire area of the circle.
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Example #4
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Example #5
a. What is the area of the
lawn that is covered by the
sprinkler?
The diagram shows the area of a lawn
covered by a water sprinkler. Round your
answer to the nearest whole number.
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Finding Complex Areas
Example #6
Find the area of the shaded region.
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Practice