Geometric ProbabilitySector – 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 - rArea of a Sector• The area of the sector

must be (N/360) times the area of the circle.

BC = 4.22 cm

mABC = 35.00

B

C

A

Geometric ProbabilityChord – 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.

mABC

circle degrees Area BC = 5.43 cm2

circle degrees = 360.00

Area BC = 55.82 cm2

Area AC = 5.43 cm2

BC = 4.22 cm

mABC = 35.00

B

C

A

Answer: or about

a. Find the area of the orange sectors.

b. Find the probability that a point chosen at random liesin 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 113.10 square units.

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.

P

Answer: The probability that a random point is on the shaded region is about 0.086 or 8.6%.

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 0.173 or

Answer: about