

10.3 Lesson: Circles and Tangents
Presentation
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Medium
Standards-aligned
Bo Gilbert
Used 17+ times
FREE Resource
15 Slides • 12 Questions
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10.3 Lesson: Circles and Tangents

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Circles and Tangents
I'm sorry that I cannot be with you for today's lesson.
A video will be added to Canvas at a later date with me going through these notes.
This activity will be taken as a grade!
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Example 1:
Q is the center of this triangle.
a) Name the circle:
b) Name a radius shown:
c) What is the length of the radius?
d) What is the length of the diameter?
e) Name all interior points shown:
f) Name all exterior points shown:
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Example 1: Answers
Q is the center of this triangle.
a) Circle Q
b) QP, QT
c) r = 16 m
d) d = 32 m
e) Interior Points: Points R, Q, and S
f) Exterior Points: X
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Multiple Choice
A chord is a line segment with ________ on the circle.
endpoints
multiple notes
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Multiple Choice
A secant is a line that intersects 2 points and _______ into the exterior of the circle.
extends
wiggles
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Multiple Choice
A tangent is a line, line segment, or ray that intersects a circle at one _______.
point
plane
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9
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Example 2:
Name Examples of each.
a) Center:
b) All Radii:
c) All Chords:
d) All Secants:
e) Diameter:
f) Tangent:
g) Point of Tangency:
h) Interior Points:
i) Exterior Points
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Example 2: Answers
a) Point O
b) ON, OR, and OM
c) MN and MT
d) MT
e) MN
f) PS
g) Point Q
h) Interior Points: B, I and O
i) Exterior Points: P and S
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Tangents Line to Circle Theorem
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
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Multiple Choice
By the Tangent Line to Circle Theorem, m∠CBA = 90° . Use Pythagorean's Theorem to find the value of CA.
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8
169
119
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Multiple Choice
Now that you know the length of CA, what is the length of x in this picture/
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8
7
13
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External tangent Congruence Theorem
If two segments from the same exterior point are tangent to a circle, then they are congruent.
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Multiple Choice
(Example 4) By the External Tangent Congruence Theorem, QP = RP. Use this information to find the value of x.
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27
3
30
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External Tangent Congruence Theorem
When circles are inscribed in polygons, the polygons are said to be circumscribed polygons. For these polygons, each side is tangent to the circle!
Recall that inscribed means drawn inside and circumscribed means drawn around.
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Example 5
ΔTRW is circumscribed about Circle A. The perimeter of ΔTRW is 50, TK = 3, and WM = 9.5. our goal is to find the length of TR.
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Example 5
By the External Tangent Congruence Theorem, since TK = 3, we know that TL = 3 also.
TK and TL are both tangent to Circle A from the same point T, so TL = TK.
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Example 5
Likewise, WK = WM and RL = RM.
The next slide has to solution to Example 5.
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Multiple Choice
(Example 6) in the figure RP
is tangent to circle Q at point R. Find the radius of circle Q.
10
100
144
12
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Multiple Choice
(Example 7) Find the value of x.
30.5
61
17.5
36
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Multiple Choice
(Example 7) Find the value of m∠ABC.
90
45
30
60
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Multiple Choice
(Example 7) Find the value of BC.
20
40
400
200
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Multiple Choice
(Example 7) Find the diameter of circle C.
20 π
40 π
10 π
400 π
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Multiple Choice
(Example 8) Find the perimeter of the polygon that circumscribes the circle.
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10.3 Lesson: Circles and Tangents

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