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Lesson 10-1

Lesson 10-1. Introduction to Circles. y. x. Circles - Terms. Circumference. 90°. Diameter (d). Radius (r). 0°. 180°. Center. Chord. 270°. Circumference = 2 π r = d π. Objectives. Identify and use parts of circles circle center radii, r chords diameter (2r = d): longest chord

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Lesson 10-1

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  1. Lesson 10-1 Introduction to Circles

  2. y x Circles - Terms Circumference 90° Diameter (d) Radius (r) 0° 180° Center Chord 270° Circumference = 2πr = dπ

  3. Objectives • Identify and use parts of circles • circle • center • radii, r • chords • diameter (2r = d): longest chord • Solve problems involving the circumference of a circle • formulas: C = 2πr or C = dπ

  4. Vocabulary • Circle – the locus (set) of all points in a plane equidistant for a given point • Center – the central point of a circle • Chord – any segment that endpoints are on the circle • Diameter – a chord that passes through the center of the circle • Radius – any segment that endpoints are the center and a point on the circle • Circumference – perimeter of a circle

  5. Answer: The circle has its center at E, so it is named circle E, or . Answer: Four radii are shown: . Answer: Four chords are shown: . Answer: are the only chords that go through the center. So, are diameters. Example 1-1a a. Name the circle. b. Name the radius of the circle. c. Name a chord of the circle. d. Name a diameter of the circle.

  6. 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

  7. Circle R has diameters and . Example 1-2a a. If ST =18, find RS. Formula for radius Substitute and simplify. Answer: 9 b. If RM =24, find QM. Formula for diameter Substitute and simplify. Answer: 48 c. If RN =2, find RP. Answer: So, RP=2. Since all radii are congruent, RN=RP.

  8. 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

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

  10. 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

  11. The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Since the diameter of , EF = 22. is part of . Since is a radius of Example 1-3c Find XF. Answer: 11 mm

  12. 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.

  13. Answer: Answer: Example 1-4a a. Find C if r=13 inches. Circumference formula Substitution b. Find C if d=6 millimeters. Circumference formula Substitution

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

  15. 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.

  16. Summary & Homework • Summary: • Diameter of a circle is twice the radius • Circumference, C, of a circle with diameter, d, or a radius, r, can be written in the form C = πd or C = 2πr • Homework: pg 526-527; 16-20, 32, 33, 44-47

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