1. Chapter 10-5
Tangents

2. Use properties of tangents. tangent
Solve problems involving circumscribed polygons.
point of tangency
Standard 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 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Key)
Lesson 5 MI/Vocab

3. Reminder
Tangent—a 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. Find Lengths
Because y is the length of the diameter, ignore the negative result. Thus, y is twice QR or y = 2(12) = 24.
Lesson 5 Ex1

8. A. 15
B. 20
C. 10
D. 5 A B C D
Lesson 5 CYP1

9. Identify Tangents
Because the converse of the Pythagorean Theorem did not prove true in this case, ΔABC is not a right triangle.
Lesson 5 Ex2

10. Identify Tangents
First determine whether ΔEWD is a right triangle by using the converse of the Pythagorean Theorem.
Because the converse of the Pythagorean Theorem is true, ΔEWD is a right triangle and EWD is a right angle.
Lesson 5 Ex2

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

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

13. 12 r r 10
r = (r + 10)2
r = 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 
AC = AB A B C

15. Congruent Tangents
ALGEBRA Find x. Assume that segments that appear tangent to circles are tangent.
Lesson 5 Ex3

16. Use the value of y to find x.
Congruent Tangents
Use the value of y to find x. 10
Answer: 1
Lesson 5 Ex3

17. ALGEBRA Find a. Assume that segments that appear tangent to circles are tangent.
Lesson 5 CYP3

18. Interactive Lab: Tangents and Communication Signals
Triangles Circumscribed About a Circle
Interactive Lab: Tangents and Communication Signals 16 45
= 45 18
P = = 158
Lesson 5 Ex4

19. A. 86
B. 180
C. 172
D. 162 A B C D
Lesson 5 CYP4

20. Common External Tangent
Common Internal Tangent

21. Homework
Ch 10-5
Pg 593
5 – 22, 30, 31, 43 – 46