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Section 7.6: Circles and Arcs Section 7.7: Areas of Circles, Sectors, and Segments

Section 7.6: Circles and Arcs Section 7.7: Areas of Circles, Sectors, and Segments Section 7.8: Geometric Probability. Review of Circles. You name a circle by its center point: circle P. Formulas: Area A = r 2 Circumference C = 2 r = d

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Section 7.6: Circles and Arcs Section 7.7: Areas of Circles, Sectors, and Segments

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  1. Section 7.6: Circles and Arcs Section 7.7: Areas of Circles, Sectors, and Segments Section 7.8: Geometric Probability

  2. Review of Circles You name a circle by its center point: circle P Formulas: AreaA = r2 CircumferenceC = 2r = d  = 3.141592654 . . . (on a scientific calculator) Most people use  = 3.14 P

  3. CD CX Arcs (parts of circles) An arc is made up of two points on a circle and all the points of the circle needed to connect those two points by a single path. X CD Semi-circle: half Minor arc < semicircle Major arc > semi circle symbol DCX

  4. E F A central angle is an angle whose vertex is the center of the circle. 120 L

  5. EF=120 Measure of Arc AB (degrees) = measure of the central angle Length of Arc AB (partial circumference) E F 6 cm 120 L

  6. B A P C D Identify at least one minor arcs, at least one major arcs, and both semi-circles in Circle P.

  7. Q 320 O 12 cm R S Find the measure of arc RS, the length of arc SR (in terms of ), and the length of arc SQR (in terms of π).

  8. Sectors A (0, 8) A sector of a circle is a region bounded by two radii and an arc of a circle. The pink area shows sector AXB. A sector has an area. B (8, 0) X (0, 0)

  9. C 6 cm 100 A B Find the area of shaded sector ACB in terms of .

  10. Chords A chord is a line segment joining two points on a circle. (A diameter is a special chord that passes through the circle center.) RQ and RS are chords. An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords of the circle. QRS is an inscribed angle. The measure of an inscribed angle is half the measure of its intercepted arc. Q S R

  11. Segments E A segment of a circle is a region bounded by an arc and the chord having the same endpoints as the arc. The yellow area shows a segment. F 120 24 ft L

  12. Find the area of shaded segment, in terms of , then rounded to the nearest tenth. E F 120 4 ft L

  13. Circle S has a diameter of 10 in and an inscribed square. Find the area of the shaded regions in terms of . 10 in S

  14. Find the area of the shaded region. Round to the nearest whole number. 13 cm 60

  15. Find the area of the shaded region. Round to the nearest whole number. 22 in 90

  16. Find the area of the shaded region. Express your answer in terms of . 7 m

  17. Geometric Probability Instead of the ratio of favorable outcomes to total possibilities, compare the target area to the entire area. d = 12 in A dart lands on a random point on the circular target shown. What is the probability that it lands on the 3-in square bull’s-eye?

  18. A park contains two circular playgrounds. One has a diameter of 60 m and the other has a diameter of 40 m. How much greater is the area of the larger playground? (Round to the nearest whole number.) A circle has an 8-in radius. Find the area of a sector whose arc measure is 135. Express your answer in terms of .

  19. Homework 7.6-7.7 Walsh Worksheet

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