ExplanationIn order to find the circumference of the circle, we need the radius, since circumference = 2πr. Both OA and OB are radii of the circle.

Triangle OAB is an equilateral triangle:If ∠O is 60°, then ∠A + ∠B = 120°, because

∠O + ∠A + ∠B = 180°

60° + ∠A + ∠B = 180°

∠A + ∠B = 120°

∠A and ∠B are equal because triangles that have two vertices on the circle and one at the center of the circle are always isosceles triangle. So 120° ÷ 2 = 60°.

Thus, ∠O is 60°, ∠A is 60°, and ∠B is 60°. Triangle OAB is an equilateral triangle.

The perimeter of triangle ΔOAB is 6. Because each side of an equilateral triangle is of equal length, both OA and OB = 2 (length of 6 ÷ 3 sides = length of 2).

Now find the circumference:

C = 2πr → C = 2π2 → C = 4π → C = 4 × (3.14) → C = 12.56

Compare the quantities:

Quantity A: 12.56

Quantity B: 12

Hence option A is correct.
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Sandy

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