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
Answer: The circle has its center at E, so it is named circle E, or . Example 1-1a Name the circle.
Answer: Four radii are shown: . Example 1-1b Name the radius of the circle.
Answer: Four chords are shown: . Example 1-1c Name a chord of the circle.
Answer: are the only chords that go through the center. So, are diameters. Example 1-1d Name a diameter of the circle.
a. Name the circle.b. Name a radius of the circle. c. Name a chord of the circle. d. Name a diameter of the circle. Answer: Answer: Answer: Answer: Example 1-1e
Circle R has diameters and . If ST18, find RS. Example 1-2a Formula for radius Substitute and simplify. Answer: 9
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
Since the diameter of , EF = 22. is part of . Since is a radius of Example 1-3d Answer: 11 mm
The diameters of , and are 5 inches, 9 inches, and 18 inches respectively. a. Find AC. b. Find EB. Example 1-3e Answer: 6.5 in. Answer: 13.5 in.
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.
MULTIPLE-CHOICE TEST ITEM Find the exact circumference of . A B C D Example 1-5a Read the Test ItemYou are given a figure that involves a right triangle and a circle. You are asked to find the exact circumference of the circle.
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
Find the exact circumference of . A B C D Example 1-5d Answer: C
Lesson 2 Contents Example 1Measures of Central Angles Example 2Measures of Arcs Example 3Circle Graphs Example 4Arc Length
ALGEBRA Refer to . Find . Example 2-1a
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
ALGEBRA Refer to . Find . Example 2-1c
form a linear pair. Example 2-1d Linear pairs are supplementary. Substitution Simplify. Subtract 140 from each side. Answer: 40
ALGEBRA Refer to . a. Find m b. Find m Example 2-1e Answer: 65 Answer: 40
In bisects and Find . Example 2-2a
is a minor arc, so is a semicircle. is a right angle. Example 2-2b Arc Addition Postulate Substitution Subtract 90 from each side. Answer: 90
In bisects and Find . Example 2-2c
since bisects . is a semicircle. Example 2-2d Arc Addition Postulate Subtract 46 from each side. Answer: 67
In bisects and Find . Example 2-2e
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
The sum of the percents is 100% and represents the whole. Use the percents to determine what part of the whole circle each central angle contains. Answer: Example 2-3b
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?
The arc for the wedge named Youth represents 26% or of the circle. The combined wedges named Other and Comfort represent . Since º, the arcs are not congruent. Example 2-3d Answer: no
SPEED LIMITS This graph shows the percent of U.S. states that have each speed limit on their interstate highways. Example 2-3e
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