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Warm-Up Exercises 1. What measure is needed to find the circumference or area of a circle? ANSWER radius or diameter 2. Find the radius of a circle with diameter 8 centimeters. ANSWER 4 cm Warm-Up Exercises 3. A right triangle has legs with lengths 5 inches and 12 inches. Find the length of the hypotenuse. ANSWER 13 in. 4. Solve 6x + 15 = 33. ANSWER 3 Warm-Up Exercises 5. Solve (x + 18)2 = x2 + 242. ANSWER 7 Warm-Up1Exercises EXAMPLE 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. a. AC SOLUTION a. AC is a radius because C is the center and A is a point on the circle. Warm-Up1Exercises EXAMPLE 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. Warm-Up1Exercises EXAMPLE 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. c. DE SOLUTION c. DE is a tangent ray because it is contained in a line that intersects the circle at only one point. Warm-Up1Exercises EXAMPLE 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. d. AE SOLUTION d. AE is a secant because it is a line that intersects the circle in two points. Warm-Up Exercises GUIDED PRACTICE for Example 1 1. In Example 1, what word best describes AG ? CB ? SOLUTION AG Is a chord because it is a segment whose endpoints are on the circle. CB is a radius because C is the center and B is a point on the circle. Warm-Up Exercises GUIDED PRACTICE 2. for Example 1 In Example 1, name a tangent and a tangent segment. SOLUTION A tangent is DE A tangent segment is DB Warm-Up2Exercises EXAMPLE Find lengths in circles in a coordinate plane Use the diagram to find the given lengths. a. Radius of b. c. Diameter of A d. Diameter of Radius of A B B SOLUTION a. The radius of A is 3 units. b. The diameter of A is 6 units. c. The radius of d. The diameter of B is 4 units. B is 2 units. Warm-Up Exercises 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. Warm-Up3Exercises EXAMPLE Draw common tangents Tell how many common tangents the circles have and draw them. a. c. b. SOLUTION a. 4 common tangents b. 3 common tangents Warm-Up3Exercises EXAMPLE Draw common tangents Tell how many common tangents the circles have and draw them. c. SOLUTION c. 2 common tangents Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 4. SOLUTION 2 common tangents Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 5. SOLUTION 1 common tangent Warm-Up Exercises GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 6. SOLUTION No common tangents Warm-Up4Exercises EXAMPLE Verify a tangent to a circle In the diagram, PT is a radius of tangent to P ? P. Is ST SOLUTION Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 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. Warm-Up5Exercises EXAMPLE 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 = r2 + 802 r2 + 100r + 2500 = r2 + 6400 100r = 3900 r = 39 ft . Substitute. Multiply. Subtract from each side. Divide each side by 100. Warm-Up6Exercises EXAMPLE Find the radius of a circle RS is tangent to C at S and RT is tangent to Find the value of x. C at T. SOLUTION RS = RT Tangent segments from the same point are 28 = 3x + 4 Substitute. 8=x Solve for x. Warm-Up Exercises GUIDED PRACTICE 7. Is DE tangent to ANSWER Yes for Examples 4, 5 and 6 C? Warm-Up Exercises GUIDED PRACTICE 8. for Examples 4, 5 and 6 ST is tangent to Q.Find the value of r. ANSWER r=7 Warm-Up Exercises GUIDED PRACTICE 9. for Examples 4, 5 and 6 Find the value(s) of x. ANSWER +3 = x Daily Homework Quiz Warm-Up Exercises 1. Give the name that best describes the figure . a. CD ANSWER c. b. secant ANSWER ANSWER d. FD chord AB tangent EP ANSWER radius Daily Homework Quiz Warm-Up Exercises 2. Tell how many common tangents the circles have . ANSWER One tangent; it is a vertical line through the point of tangency. Daily Homework Quiz Warm-Up Exercises 3. Is AB tangent to . C? Explain. ANSWER 2 2 2 Yes; 16 + 30 = 1156 = 34 so AB AC, and a line radius at its endpoint is tangent to the circle. to a Daily Homework Quiz Warm-Up Exercises 4. Find x. ANSWER 12