1. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AC a.
SOLUTION
is a radius because C is the center and A is a point on the circle. AC a.

2. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. b. AB
SOLUTION b. AB
is a diameter because it is a chord that contains the center C.

3. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. DE c.
SOLUTION c. DE
is a tangent ray because it is contained in a line that intersects the circle at only one point.

4. EXAMPLE 1
Identify special segments and lines
Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AE d.
SOLUTION d. AE
is a secant because it is a line that intersects the circle in two points.

5. GUIDED PRACTICE
for Example 1
1. In Example 1, what word best describes
AG ? CB ?
SOLUTION
Is a chord because it is a segment whose endpoints are on the circle. AG CB
is a radius because C is the center and B is a point on the circle.

6. GUIDED PRACTICE
for Example 1
2. In Example 1, name a tangent and a tangent segment.
SOLUTION
A tangent is DE
A tangent segment is DB

7. EXAMPLE 2
Find lengths in circles in a coordinate plane
Use the diagram to find the given lengths. a.
Radius of A b.
Diameter of A
Radius of B c.
Diameter of B d.
SOLUTION a.
The radius of A is 3 units. b.
The diameter of A is 6 units. c.
The radius of B is 2 units. d.
The diameter of B is 4 units.

8. GUIDED PRACTICE
for Example 2
3. Use the diagram in Example 2 to find the radius and diameter of C and D.
SOLUTION a.
The radius of C is 3 units. b.
The diameter of C is 6 units. c.
The radius of D is 2 units. d.
The diameter of D is 4 units.

9. EXAMPLE 3
Draw common tangents
Tell how many common tangents the circles have and draw them. a. b. c.
SOLUTION a.
4 common tangents
3 common tangents b.

10. EXAMPLE 3
Draw common tangents
Tell how many common tangents the circles have and draw them. c.
SOLUTION c.
2 common tangents

11. GUIDED PRACTICE
for Example 3
Tell how many common tangents the circles have and draw them. 5.
SOLUTION
1 common tangent

12. GUIDED PRACTICE
for Example 3
Tell how many common tangents the circles have and draw them. 6.
SOLUTION
No common tangents

13. EXAMPLE 4
Verify a tangent to a circle
In the diagram, PT is a radius of P. Is ST tangent to P ?
SOLUTION
Use the Converse of the Pythagorean Theorem. Because = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

14. Find the radius of a circle
EXAMPLE 5
Find the radius of a circle
In the diagram, B is a point of tangency. Find the radius r of C.
SOLUTION
You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem.
AC2 = BC2 + AB2
Pythagorean Theorem
(r + 50)2 = r
Substitute.
r r = r
Multiply.
100r = 3900
Subtract from each side.
r = 39 ft .
Divide each side by 100.

15. Find the radius of a circle
EXAMPLE 6
Find the radius of a circle
RS is tangent to C at S and RT is tangent to C at T. Find the value of x.
SOLUTION
RS = RT
Tangent segments from the same point are
28 = 3x + 4
Substitute.
8 = x
Solve for x.

16. GUIDED PRACTICE
for Examples 4, 5 and 6
7. Is DE tangent to C?
ANSWER
Yes

17. GUIDED PRACTICE
for Examples 4, 5 and 6
8. ST is tangent to Q.Find the value of r.
ANSWER
r = 7

18. GUIDED PRACTICE
for Examples 4, 5 and 6
9. Find the value(s) of x.
+3 = x
ANSWER

19. Daily Homework Quiz 1.
Give the name that best describes the figure . a. CD b. AB
ANSWER
secant
ANSWER
tangent c. FD d. EP
ANSWER
chord
ANSWER
radius

20. Daily Homework Quiz
Is AB tangent to C? Explain. . 3.
ANSWER
Yes; = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle. 2

21. Daily Homework Quiz 4.
Find x.
ANSWER 12
ANSWER 12