EXAMPLE 1

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

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

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

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

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

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

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

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

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

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

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

12. 6. for Example 3 GUIDED PRACTICE Tell how many common tangents the circles have and draw them. SOLUTION Nocommon tangents

13. In the diagram, PTis a radius of P. Is STtangent to P ? SOLUTION Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372,PSTis a right triangle and STPT. So, STis perpendicular to a radius of Pat its endpoint on P. By Theorem 10.1, STis tangent to P. EXAMPLE 4 Verify a tangent to a circle

14. In the diagram, Bis a point of tangency. Find the radiusr of C. SOLUTION You know from Theorem 10.1 that AB BC, so ABCis a right triangle. You can use the Pythagorean Theorem. EXAMPLE 5 Find the radius of a circle AC2 = BC2 + AB2 Pythagorean Theorem (r + 50)2 = r2 + 802 Substitute. r2 + 100r + 2500 = r2 + 6400 Multiply. 100r = 3900 Subtract from each side. r = 39 ft. Divide each side by 100.

15. RSis tangent to Cat Sand RTis tangent to Cat T. Find the value of x. Tangent segments from the same point are EXAMPLE 6 Find the radius of a circle SOLUTION RS= RT 28 = 3x + 4 Substitute. 8 = x Solve for x.

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

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

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

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

20. Is AB tangent to C? Explain. . ANSWER Yes; 16 + 30 = 1156 = 34 so AB AC, and a line to a radius at its endpoint is tangent to the circle. 2 2 2 Daily Homework Quiz 3.

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