1. Lesson 10-1 Introduction to Circles

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

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

6. Example 1-1e Answer: 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:

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

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

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

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

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

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

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

15. 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 1-4e Answer:

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