1. Warm-Up Exercises 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with diameter 8 centimeters. ANSWER radius or diameter ANSWER 4 cm

2. Warm-Up Exercises 3. A right triangle has legs with lengths 5 inches and 12 inches. Find the length of the hypotenuse. 4. Solve 6x + 15 = 33. ANSWER 3 13 in.

3. Warm-Up Exercises 5. Solve (x + 18) 2 = x 2 + 24 2. ANSWER 7

4. Warm-Up Exercises 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.

5. Warm-Up Exercises EXAMPLE 1 Identify special segments and lines b. AB 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 SOLUTION

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

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

8. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 1 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. 1. In Example 1, what word best describes AG ? CB ?

9. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 1 2. In Example 1, name a tangent and a tangent segment. A tangent is DE A tangent segment is DB

10. Warm-Up Exercises EXAMPLE 2 Find lengths in circles in a coordinate plane b. Diameter of A Radius of B c. Diameter of B d. Use the diagram to find the given lengths. a.Radius of A 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.

11. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 2 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. 3. Use the diagram in Example 2 to find the radius and diameter of C and D.

12. Warm-Up Exercises 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.

13. Warm-Up Exercises EXAMPLE 3 Draw common tangents c. 2 common tangents Tell how many common tangents the circles have and draw them. c. SOLUTION

14. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 4. 2 common tangents

15. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 1 common tangent 5.

16. Warm-Up Exercises SOLUTION GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. No common tangents 6.

17. Warm-Up Exercises EXAMPLE 4 Verify a tangent to a circle SOLUTION Use the Converse of the Pythagorean Theorem. Because 12 2 + 35 2 = 37 2, 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. In the diagram, PT is a radius of P. Is ST tangent to P ?

18. Warm-Up Exercises 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. AC 2 = BC 2 + AB 2 (r + 50) 2 = r 2 + 80 2 r 2 + 100r + 2500 = r 2 + 6400 100r = 3900 r = 39 ft. Pythagorean Theorem Substitute. Multiply. Subtract from each side. Divide each side by 100.

19. Warm-Up Exercises 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 28 = 3x + 4 8 = x Substitute. Solve for x. Tangent segments from the same point are

20. Warm-Up Exercises GUIDED PRACTICE for Examples 4, 5 and 6 7. Is DE tangent to C ? ANSWER Yes

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

22. Warm-Up Exercises GUIDED PRACTICE for Examples 4, 5 and 6 9. Find the value(s) of x. + 3 = x ANSWER

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

24. Warm-Up Exercises Daily Homework Quiz 2. Tell how many common tangents the circles have. ANSWER One tangent; it is a vertical line through the point of tangency.

25. Warm-Up Exercises Daily Homework Quiz 3. 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. 222

26. Warm-Up Exercises Daily Homework Quiz 4. Find x. ANSWER 12 ANSWER 12