Chapter 7
Circles
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Applied Geometry – CH 06 – Quadrilaterals
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Chapter 7 Pacing and Assignments
#days Topic
Vocabulary Introduction
1
Lesson 7.1 – Circle Basics
Practice 7.1 #1-5
2
Lesson 7.2 – Central Angles and Arcs
Practice 7.2 #1-12
Practice 7.2 #13-24
2
Lesson 7.3 – Inscribed Angles
Practice 7.3 #1-10
Practice 7.3 #11-14
2
Lesson 7.4 – Circumference and Arc Length
Practice 7.4(a) #8-42 (e)
Practice 7.4(b) #2-28 (e)
2
Lesson 7.5 – Areas of Circles and Sectors
Practice 7.5(a) #6-36 (e)
Practice 7.5(b) #2-16(e)
1
Lesson 7.6 – Circles on the Coordinate Plane
Practice 7.6 #1-14, 23,24
Chapter 7 Exam – Circles
Applied Geometry – CH 06 – Quadrilaterals
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Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.1 – Circle Basics
Lesson Notes
A _____________________ is the set of all points equidistant from a given point,
called the center.
A _____________________ is a segment that connects the center to a point on the circle.
(all radii in a circle are congruent).
A _____________________ is a segment that connects two points on the circle and goes
through the center. (diameter = 2 radius, or d=2r)
A _____________________ is a segment whose endpoints are on a circle. (a
diameter is an example of a chord).
Example
Name each of the following for circle R.
All diameters:
All Radii:
All chords:
A _____________________ to a circle is a line that intersects the circle at
exactly one point.
A _____________________ is a line that intersects a circle at two points. (a
secant contains a chord).
Example
Name each of the following for circle A.
All secants
All tangents
All diameters
All chords
All radii
_________________________________ two circles that lie on the same plane
and have the same center.
Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.2 – Central Angles and Arcs
Lesson Notes
A ________________________________ is an angle whose vertex is the
center of the circle.
An ___________________ is a part of a circle.
Three Types of Arcs:
1. Semicircle:
2. Minor arc:
3. Major arc:
The measure of an arc is equal to the measure of the central angle
that goes with it.
_____________________________________: two arcs on the same circle that have exactly
one point in common.
Example
Applied Geometry – CH 06 – Quadrilaterals
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Example
Example
Example
Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.3 – Inscribed Angles
Lesson Notes
∡ B is an inscribed angle
B is on a circle and sides
and
are chords
AC is the intercepted arc of ∡ B
Theorem
__________________________________________________________________________________
__________________________________________________________________________________
Corollaries:
1. Two inscribed angles that intercept the same arc are congruent.
2. An angle inscribed in a semicircle is a right angle.
Example
Applied Geometry – CH 06 – Quadrilaterals
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Example
Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.4 – Circumference and Arc Length
Lesson Notes
_____________________________ of a circle is the distance around the outside.
Example
Find the circumference of circle P in terms of
and to the nearest tenth.
Example
Find the circumference of a circle whose diameter measures 24 inches to the nearest
hundredth.
Example
If the circumference of a circle is
meters, what is the radius of the circle?
Example
The wheel of an adult’s bicycle has a diameter of 26 inches. The wheel of a child’s
bicycle has a diameter 18 inches. To the nearest inch, how much further does the larger
bicycle wheel travel in one revolution than the smaller bicycle wheel?
_________________________________ is found by using a fraction of the circumference.
Example
Find the length of a semicircle with a radius of 5 meters, in terms of .
Applied Geometry – CH 06 – Quadrilaterals
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Example
In terms of , find the length of arc AB if CB = 24 inches.
Example
Find the length of arc CDE to the nearest tenth if CP = 9 inches.
Example
Find the length of the arc marked.
Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.5 – Areas of Circles and Sectors
Lesson Notes
Area of a circle:
Example
Find the area of a circle with a diameter of 12 meters in terms of .
Example
Example
Some farmers use a circular irrigation method. An irrigation arm acts as the radius of an
irrigation circle. How much more land is covered with an irrigation arm of 300 feet than by
an irrigation arm of 250 feet?
Example
What is the difference in areas of a circular table with a diameter 6 feet and a circular
table with a diameter 8 feet?
A __________________________________________ is the region bounded by two radii and
their intercepted arc.
The shaded region is a sector of circle O.
Applied Geometry – CH 06 – Quadrilaterals
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Example
Applied Geometry – CH 06 – Quadrilaterals
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Lesson 7.6 – Circles in the Coordinate Plane
Lesson Notes
Write the equation of the circle centered at (2,3) with a radius of 5.
By the definition of a circle, every point on the circle will be 5 units
from the center (2,3).
Using the distance formula:
*** The equation of a circle centered at (h,k) with a radius of r is:
** When the circle is centered at the origin:
Example
Find the center and radius of each:
1. (x + 9)2 + (y – 7)2 = 121
2. x2 + y2 = 5
3. 3x2 + 3y2 = 27
Example
Write the equation of a circle with center (-8,2) and a radius of 9.
Example
Write the equation of the circle that has a diameter with endpoints of (-9,3) and (1,7)
Example
Write the equation of the circle that has a center of (-10,8) and goes through the point
(1,-4).
Applied Geometry – CH 06 – Quadrilaterals
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