
Tangent Rule
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
9 Slides • 21 Questions
1
Theorems about Tangent Lines
Directions:
Take notes on the theorems.
Copy the problems into your notes.
For this lesson, assume all tangent lines that appear tangent are tangent, UNLESS the question asks you to prove it is tangent.
2
3
Radius-Tangent Theorem
The tangent to a circle is perpendicular to the radius at the point of contact.
This means that right triangles are present!
4
Multiple Choice
Segment ED is tangent to circle O. What is the value of x?
*Hint: All the angles in a triangle make 180 degrees, and because DE is a tangent line, the angle at D is 90 degrees!
232
52
79
115
5
Multiple Choice
6
Multiple Choice
Determine y.
30
60
90
180
7
Multiple Choice
Assume both lines are tangent to circle O. What is the value of x?
90
115
120
45
8
9
Multiple Choice
Find the length of the missing segment. Let x be the hypotenuse.
12
34
169
13
10
Multiple Choice
#1 Line AB is tangent to circle C. Find the value of x.
98.18
117
153.3
108
11
Open Ended
What is the radius of circle O?
Be careful with this one. Your equation should be:
x^2 + 10^2 = (x+6)^2
Which is a quadratic equation!
12
Circle Theorem
Two tangents from a point to a circle are equal.
***This means we set the expressions equal to each other!
13
14
Multiple Choice
What is the value of x?
x=24
x=12
x=8
x=6
15
Multiple Choice
What is the value of x?
x=24
x=12
x=7
x=6
16
Multiple Choice
How can we solve for x in this example?
add both expressions together and subtract from 360
set both expressions equal to each other
use Pythagorean Theorem
use magic
combine like terms
17
Solve for x.
3x - 10 = 2x +5
x - 10 = 5
x = 15
18
Fill in the Blanks
Type answer...
19
20
21
Multiple Choice
Assume that all the lines that appear tangent are tangent. Find the perimeter of the triangle.
54
42
36
22
Multiple Choice
Assume that all the lines that appear tangent are tangent. Find the perimeter of the triangle.
58.8
61
80.2
23
Multiple Choice
A tangent line intersects the circle ...
in exactly two points
in exactly one point
through the center
with the diameter
24
Multiple Choice
Which shows a tangent line?
25
Multiple Choice
26
Multiple Choice
Using lines tangent to the circle, find the value of x.
57
137
47
257
27
Multiple Choice
TS is tangent to circle P. What is x?
11.2
18.0
25.0
30.0
28
Multiple Choice
29
Multiple Choice
30
Multiple Choice
Theorems about Tangent Lines
Directions:
Take notes on the theorems.
Copy the problems into your notes.
For this lesson, assume all tangent lines that appear tangent are tangent, UNLESS the question asks you to prove it is tangent.
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