Splash Screen. Contents. Lesson 10-1 Circles and Circumferences Lesson 10-2 Angles and Arcs Lesson 10-3 Arcs and Chords Lesson 10-4 Inscribed Angles Lesson 10-5 Tangents Lesson 10-6 Secants, Tangents, and Angle Measures Lesson 10-7 Special Segments in a Circle

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Contents Lesson 10-1Circles and Circumferences Lesson 10-2Angles and Arcs Lesson 10-3Arcs and Chords Lesson 10-4Inscribed Angles Lesson 10-5Tangents Lesson 10-6Secants, Tangents, and Angle Measures Lesson 10-7Special Segments in a Circle Lesson 10-8Equations of Circles

Lesson 1 Contents Example 1Identify Parts of a Circle Example 2Find Radius and Diameter Example 3Find Measures in Intersecting Circles Example 4Find Circumference, Diameter, and Radius Example 5Use Other Figures to Find Circumference

Circle R has diameters . If RM24, find QM. Example 1-2b Formula for diameter Substitute and simplify. Answer: 48

Circle R has diameters . If RN2, find RP. Example 1-2c Since all radii are congruent, RN=RP. Answer: So, RP=2.

Circle M has diameters a. If BG=25, find MG. b. If DM=29, find DN. c. If MF=8.5, find MG. Example 1-2d Answer: 12.5 Answer: 58 Answer: 8.5

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Example 1-3a Find EZ.

Since the diameter of , EF = 22. Since the diameter of FZ = 5. is part of . Example 1-3b Segment Addition Postulate Substitution Simplify. Answer: 27 mm

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Find XF. Example 1-3c

Answer: Example 1-4a Find C if r=13 inches. Circumference formula Substitution

Answer: Example 1-4b Find C if d=6 millimeters. Circumference formula Substitution

Divide each side by . Example 1-4c Find dand r to the nearest hundredth if C = 65.4 feet. Circumference formula Substitution Use a calculator.

Answer: Example 1-4d Radius formula Use a calculator.

Answer: Answer: Answer: Example 1-4e a. Find C if r = 22 centimeters. b. Find C if d = 3 feet. c. Find d and r to the nearest hundredth if C = 16.8 meters.

Example 1-5b Solve the Test ItemThe radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x. Pythagorean Theorem Substitution Simplify. Divide each side by 2. Take the square root of each side.

Example 1-5c So the radius of the circle is 3. Circumference formula Substitution Because we want the exact circumference, the answer is B. Answer: B

The sum of the measures of Use the value of x to find Example 2-1b Substitution Simplify. Add 2 to each side. Divide each side by 26. Given Substitution Answer: 52

Example 2-2f Vertical angles are congruent. Substitution. Substitution. Subtract 46 from each side. Substitution. Subtract 44 from each side. Answer: 316

In and are diameters, and bisects Find each measure. a. b. c. Example 2-2g Answer: 54 Answer: 72 Answer: 234

BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Find the measurement of the central angle representing each category. List them from least to greatest. Example 2-3a

Example 2-3c BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Is the arc for the wedge named Youth congruent to the arc for the combined wedges named Other and Comfort?

a. Find the measurement of the central angles representing each category. List them from least to greatest. b.Is the arc for the wedge for 65 mph congruent to the combined arcs for the wedges for 55 mph and 70 mph? Answer: Example 2-3f Answer: no

In and . Find the length of . In and . Write a proportion to compare each part to its whole. Example 2-4a

degree measure of arc arc length circumference degree measure of whole circle Now solve the proportion for . Multiply each side by 9 . Answer: The length of is units or about 3.14 units. Example 2-4b Simplify.

In and . Find the length of . Answer: units or about 49.48 units Example 2-4c