Theorems about Tangent Lines

Theorems about Tangent Lines

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Directions:​

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​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.

Radius-Tangent Theorem

The tangent to a circle is perpendicular to the radius at the point of contact.

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This means that right triangles are present!

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

Multiple Choice

Name a tangent.

• Segment XC
• Segment LM
• Segment HJ
• LINE BD

Multiple Choice

Determine y.

• 30

• 60

• 90

• 180

Multiple Choice

Assume both lines are tangent to circle O. What is the value of x?

• 90

• 115

• 120

• 45

Multiple Choice

Find the length of the missing segment. Let x be the hypotenuse.

• 12

• 34

• 169

• 13

Multiple Choice

#1 Line AB is tangent to circle C. Find the value of x.

• 98.18

• 117

• 153.3

• 108

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!

Circle Theorem

Two tangents from a point to a circle are equal.

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​***This means we set the expressions equal to each other!

Multiple Choice

What is the value of x?

• x=24

• x=12

• x=8

• x=6

Multiple Choice

What is the value of x?

• x=24

• x=12

• x=7

• x=6

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

Solve for x.

3x - 10 = 2x +5

x - 10 = 5

x = 15

Multiple Choice

Assume that all the lines that appear tangent are tangent. Find the perimeter of the triangle.

• 54

• 42

• 36

Multiple Choice

Assume that all the lines that appear tangent are tangent. Find the perimeter of the triangle.

• 58.8

• 61

• 80.2

Multiple Choice

A tangent line intersects the circle ...

• in exactly two points

• in exactly one point

• through the center

• with the diameter

Multiple Choice

Which shows a tangent line?

Multiple Choice

A tangent line intersecting with a radius always creates a ____________ angle

• right
• acute
• obtuse
• straight

Multiple Choice

Using lines tangent to the circle, find the value of x.

• 57

• 137

• 47

• 257

Multiple Choice

TS is tangent to circle P. What is x?

• 11.2

• 18.0

• 25.0

• 30.0

Multiple Choice

Find the radius r

• 2
• 3
• 4
• 5

Multiple Choice

What is the value of x?

• 22
• 25
• 15
• 20

Multiple Choice

Assume that all the lines that appear tangent are tangent. Find the perimeter

• 54
• 36
• 48
• 42