properties of tangents in circles

PROPERTIES OF TANGENTS IN CIRCLES Lesson 11.3

Unit 6 WB Page 32

Today's Objectives ~

By the end of the lesson you should be able to:

• Explain what a circumscribed angle is and how it is related to

a circle.

• Explain the relationship between a tangent line and the radius

of a circle.

What is a tangent line to a circle?

What is a point of tangency?

What is the relationship of the tangent line

and the radius at the point of tangency?

Which lines are tangent to the circle?

One of these pictures has a secant line. Which one?

How do we prove a line is tangent to a circle? Let's look at example 1 to find out.

Example 1 (page 33):

The opposite of this principle is also useful.

If you know that a line is tangent to a circle, then

you know it forms a right angle with the radius at

the point of tangency.

You can use this concept to find the length of the

radius, etc., as in example 4.

Example 4 (page 36):

(Even though line AB doesn't look tangent to circle C at point B, we know that it is

because it is given in the instructions.)

If the radius and the tangent line are

perpendicular at the point of tangency,

what do you know about the slopes of the two

lines?

Let's go to example 3.

Example 3 (page 35):

Here are some more interesting facts about tangent lines to circle:

Let's do Example 2 now (page 34):

Example: (Not in book)Can you find the measure of central angle CDB in the picture below? (Lines AB and

AC are tangent to circle D.)

Hint: The measures of the interior angles of a quadrilateral add up to 360o.

214° − 146° = 68°

and68°

2= 34°

Another way to think of it is that the central angle (146o) and angle formed by

the tangent lines (34o) must add up to 180o.

34o + 146o = 180o

This leads us to another little fact about tangent lines and circles:

We have to assume all lines that

might look tangent are tangent for

this problem, so the only line outside

of a circle that is not tangent is the

one from the ticket booth at point A.

Task w/coaching (page 37):

ASSIGNMENT 11.3

WB: Page 39 # 1-9

On #4, you need to assume that the base is perpendicular to the wheel.

On #5, check the length of your hypotenuse!)

RB: Page U6-39: # 1, 3-5, 7, 8