Final Answer:
The ratio of the area of sector ABC to the area of sector DBE is:
c) 2:3
Step-by-step explanation:
The ratio of the area of sector ABC to the area of sector DBE is 2:3. This can be determined by considering the relationship between the central angles of the sectors and their corresponding areas. In a circle, the ratio of the area of two sectors is equal to the ratio of their central angles.
In this case, let's denote the central angles of sector ABC and sector DBE as θ₁ and θ₂, respectively. The formula for the area of a sector is (θ/360) * π * r², where θ is the central angle and r is the radius. Since the radii are not given, they cancel out when comparing the ratios.
Now, if we compare the central angles of sector ABC and sector DBE, we find that θ₁ is twice the size of θ₂. Therefore, the ratio of their areas is 2:3.
To elaborate, if we assume θ₁ = 2x and θ₂ = x, where x is a constant, then the ratio of their areas is [(2x/360) * π * r²] : [(x/360) * π * r²], which simplifies to 2:3.
In conclusion, the correct answer is c) 2:3, indicating that the area of sector ABC is in a 2:3 ratio with the area of sector DBE based on their central angles.