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.

The true statement regarding the shaded sectors is: C. area of sector AOB = area of sector DOC because they have equal central angle measures.

What is the Area of a Sector?

The area of a sector of a circle = ∅/360 × πr², where r is the radius of the circle, and ∅ is the central angle of the sector.

Therefore, if two sectors in the same circle have the same central angle measure, the sectors have the same radius value and will therefore have the same area.

In summary, the true statement will be: C. area of sector AOB = area of sector DOC because they have equal central angle measures.

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