Explanation

In 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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Attached is a visual that should help.



Source: Vince and Brian's GRE PowerPrep Explanations

Best of luck on your GRE and beyond,

-Brian
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easy stuff

Solution:

We are given the following circle:



We are given that O is the center of the circle, and the perimeter of Δ AOB is 6. We need to determine whether the circumference of the circle (quantity A) is greater than 12 (quantity B).

We see that OA = OB = radius of the circle and that angle AOB, the angle opposite side AB, is 60. If we let angle OAB and angle OBA = x, then we have the equation:

x + x + 60 = 180

2x = 120

x = 60

Thus, we see that each angle of triangle OAB is 60, and thus triangle OAB is an equilateral triangle.

Since the perimeter of the triangle is 6, each side of the triangle is 2.

Thus, OA = OB = radius = 2.

We can now determine the circumference of the circle:

Circumference = 2πr = 2 x π x 2 = 4π ≈ 4 x 3.14 = 12.56

Since 12.56 > 12, quantity A is greater than quantity B.

Answer: A
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