Lesson 1 Contents

1
Transparency 10-5
5-Minute Check on Lesson 10-4

• Refer to the figure and find each measure.
• m?1
• m?2
• m?3
• m?4
• In ?B, find x if m?A 3x 9and m?B 8x 4.
• If an
  inscribed angle has a measure of 110, what is the
  measure of its intercepted arc?

60
20
20
100
x 11
Standardized Test Practice
55
70
110
220
A
C
B
D
D
Click the mouse button or press the Space Bar to
display the answers.
2
Lesson 10-5

• Tangents

3
Objectives

• Use properties of tangents
• Solve problems involving circumscribed polygons

4
Vocabulary

• Tangent a line that intersects a circle in
  exactly one point
• Point of tangency point where a tangent
  intersects a circle

5
Example 5-1a
6
Example 5-1b
Pythagorean Theorem
Simplify.
Subtract 256 from each side.
Take the square root of each side.
Because y is the length of the diameter, ignore
the negative result.
7
Example 5-1c
Answer 15
8
Example 5-2a
First determine whether ?ABC is a right triangle
by using the converse of the Pythagorean Theorem.
Pythagorean Theorem
Because the converse of the Pythagorean Theorem
did not prove true in this case, ?ABC is not a
right triangle.
9
Example 5-2c
First determine whether ?EWD is a right triangle
by using the converse of the Pythagorean Theorem.
Pythagorean Theorem
Simplify.
Because the converse of the Pythagorean Theorem
is true, ?EWD is a right triangle and ?EWD is a
right angle.
10
Example 5-2f
Answer no
11
Example 5-3a
ALGEBRA Find x. Assume that segments that appear
tangent to circles are tangent.
12
Example 5-3b
Definition of congruent segments
Substitution.
Use the value of y to find x.
Definition of congruent segments
Substitution
Simplify.
Subtract 14 from each side.
Answer 1
13
Example 5-4a
Use Theorem 10.10 to determine the equal measures.
Definition of perimeter
Substitution
Answer The perimeter of ?HJK is 158 units.

14
Example 5-4c
Answer 172 units
15
Summary Homework

• Summary
• A line that is tangent to a circle intersects the
  circle in exactly one point.
• A tangent is perpendicular to a radius of a
  circle
• Two segments tangent to a circle form the same
  exterior point are congruent
• Homework
• pg 556-558 8-11, 12-17