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Circle O is shown. Line segments B D and A C intersect at point O. The length of B O is 5. Angle C O D is StartFraction 4 pi Over 9 EndFraction. Sectors A O B and D O C are shaded.
Which statement is true regarding the two shaded sectors of circle O? Explain.
The area of sector AOB is greater than the area of sector DOC because the central angle measures are equal.
The area of sector DOC is greater than the area of sector AOB because the radii are equal.
The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal.
The area of sector AOB is equal to the area of sector DOC because the radii are equal.
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The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal.
Explanation: A and C are opposite points on a line through the center and B and D are opposite points, so OA and OC are in opposite directions and OB and OD are in opposite directions. The angle between OA and OB equals the angle between OC and OD, so ∠AOB = ∠COD = 4π/9. Since both sectors have the same radius and the same central angle, their areas (½ r^2 θ) are equal.
Explanation: A and C are opposite points on a line through the center and B and D are opposite points, so OA and OC are in opposite directions and OB and OD are in opposite directions. The angle between OA and OB equals the angle between OC and OD, so ∠AOB = ∠COD = 4π/9. Since both sectors have the same radius and the same central angle, their areas (½ r^2 θ) are equal.
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