Geometric Probability Sector – A region of a circle bounded by an arc of the circle and the two radii to the arc’s endpoints. Two important quantities relative to sectors: 1.Central angle measure – N 2.Radius length - r Area of a Sector The area of the sector must be (N/360) times the area of the circle.

Geometric Probability Chord – A segment joining two points on a circle. Segment – The region of a circle bounded by an arc and a chord. Area of a Segment Subtract the area of the triangle from the area of the sector. m  ABC circle degrees    AreaBC  =5.43 cm 2 circle degrees =  AreaBC =55.82 cm 2 AreaAC =5.43 cm 2 BC =4.22 cm m  ABC =35.00  B C A

Example 5-2c Answer: or about a. Find the area of the orange sectors. b. Find the probability that a point chosen at random lies in the orange region. Answer: or about 0.33

Divide the area of the shaded regions by the area of the circle to find the probability. First, find the area of the circle. The radius is 6, so the area is or about square units. Example 5-3b A regular hexagon is inscribed in a circle with a diameter of 12. Find the probability that a point chosen at random lies in the shaded regions.

Example 5-3b P Answer:The probability that a random point is on the shaded region is about or 8.6%.

Example 5-3c A regular hexagon is inscribed in a circle with a diameter of 18. a. Find the area of the shaded regions. b. Find the probability that a point chosen at random lies in the shaded regions. Answer:about or Answer:about