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Circles and Arcs

. Circles and Arcs. Lesson 10-6. Day 2 Warmup. 1. A circle graph has a section marked “Potatoes: 28%.” What is the measure of the central angle of this section? 2. Explain how a major arc differs from a minor arc. Use O for Exercises 3–6. 3. Find mYW . 4. Find mWXS.

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Circles and Arcs

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  1. . Circles and Arcs Lesson 10-6 Day 2 Warmup 1. A circle graph has a section marked “Potatoes: 28%.” What is the measure of the central angle of this section? 2. Explain how a major arc differs from a minor arc. Use O for Exercises 3–6. 3. Find mYW. 4. Find mWXS. 100.8 A major arc is greater than a semicircle. A minor arc is smaller than a semicircle. 30 270 10-6

  2. The irrational number is defined as the ratio of the circumference C to the diameter d, or Circles and Arcs Lesson 10-6 Notes Solving for C gives the formula C = d. Also d = 2r, so C = 2r. 10-6

  3. Helpful Hint The key gives the best possible approximation for on your calculator. Always wait until the last step to round. Circles and Arcs Lesson 10-6 Notes 10-6

  4. The measure of an arc is in degrees while the arc length is a fraction of a circle’s circumference. An arc of 60 represents or of the circle. Its arc length is the circumference of the circle. This observation suggests the following theorem. Circles and Arcs Lesson 10-6 Notes 10-6

  5. Circles and Arcs Lesson 10-6 Notes It is possible for two arcs of different circles to have the same measure but different lengths, as shown below. It is also possible for two arcs of different circles to have the same length but different measures. Congruent arcs are arcs that have the same measure and are in the same circle or in congruent circles 10-6

  6. A circular swimming pool with a 16-ft diameter will be enclosed in a circular fence 4 ft from the pool. What length of fencing material is needed? Round your answer to the next whole number. Draw a diagram of the situation. C = dFormula for the circumference of a circle C = (24) Substitute. C 3.14(24) Use 3.14 to approximate . C 75.36 Simplify. Circles and Arcs Lesson 10-6 Additional Examples Real-World Connection The pool and the fence are concentric circles. The diameter of the pool is 16 ft, so the diameter of the fence is 16 + 4 + 4 = 24 ft. Use the formula for the circumference of a circle to find the length of fencing material needed. Quick Check About 76 ft of fencing material is needed. 10-6

  7. . Find the length of ADB in M in terms of . Because mAB = 150, mADB = 360 – 150 = 210. Arc Addition Postulate 210 360 mADB 360 length of ADB = • 2 rArc Length Formula length of ADB = • 2 (18) Substitute. length of ADB = 21 The length of ADB is 21 cm. Circles and Arcs Lesson 10-6 Additional Examples Finding Arc Length Quick Check 10-6

  8. 1. A circle graph has a section marked “Potatoes: 28%.” What is the measure of the central angle of this section? 2. Explain how a major arc differs from a minor arc. Use O for Exercises 3–6. 3. Find mYW. 4. Find mWXS. 5. Suppose that P has a diameter 2 in. greater than the diameter of O. How much greater is its circumference? Leave your answer in terms of . 6. Find the length of XY. Leave your answer in terms of . . . . 2 9 Circles and Arcs Lesson 10-6 Lesson Quiz 100.8 A major arc is greater than a semicircle. A minor arc is smaller than a semicircle. 30 270 10-6

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