Tangents

1
Chapter 10-5

• Tangents

2
Lesson 5 MI/Vocab

• tangent

• Use properties of tangents.

• Solve problems involving circumscribed polygons.

• point of tangency

Standard 7.0 Students prove and use theorems
involving the properties of parallel lines cut by
a transversal, the properties of quadrilaterals,
and the properties of circles. (Key) Standard
21.0 Students prove and solve problems regarding
relationships among chords, secants, tangents,
inscribed angles, and inscribed and circumscribed
polygons of circles. (Key)
3
Reminder

• Tangenta line that intersects the circle in only
  one point

4
Secant
Tangent
Diameter
Radius
Point of Tangency
Chord
5
Tangent Theorem

• A line is tangent to a circle ? it is ? to a
  radius at its endpoint on the circle

6
Examples
7
Lesson 5 Ex1
Find Lengths
Because y is the length of the diameter, ignore
the negative result. Thus, y is twice QR or y
2(12) 24.
8
Lesson 5 CYP1
A. 15 B. 20 C. 10 D. 5

1. A
2. B
3. C
4. D

9
Lesson 5 Ex2
Identify Tangents
Because the converse of the Pythagorean Theorem
did not prove true in this case, ?ABC is not a
right triangle.
10
Lesson 5 Ex2
Identify Tangents
First determine whether ?EWD is a right triangle
by using the converse of the Pythagorean Theorem.
Because the converse of the Pythagorean Theorem
is true, ?EWD is a right triangle and ?EWD is a
right angle.
11
Lesson 5 CYP2
A. yes B. no C. cannot be determined

1. A
2. B
3. C

12
Lesson 5 CYP2
A. yes B. no C. cannot be determined

1. A
2. B
3. C

13
12
r
10
r
r2 122 (r 10)2 r2 144 r2 20r
100 144 20r 100 44 20r r
14

• If two segments from the same external point are
  tangent to a circle ? they are ?

15
Lesson 5 Ex3
Congruent Tangents
ALGEBRA Find x. Assume that segments that appear
tangent to circles are tangent.
16
Lesson 5 Ex3
Congruent Tangents
Use the value of y to find x.
Answer 1
17
Lesson 5 CYP3
ALGEBRA Find a. Assume that segments that appear
tangent to circles are tangent.
A. 6 B. 4 C. 30 D. 6

1. A
2. B
3. C
4. D

18
Lesson 5 Ex4
Triangles Circumscribed About a Circle
Interactive Lab Tangents and Communication
Signals
16
45
16 29 45
18
P 16 18 18 45 45 16 158
19
Lesson 5 CYP4
A. 86 B. 180 C. 172 D. 162

1. A
2. B
3. C
4. D

20
Common External Tangent
Common Internal Tangent
21
Homework

• Ch 10-5
• Pg 593
• 5 22, 30, 31, 43 46