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Given that Angle CAO = 60
We know OA=OC=radius, So angle ACO=60(equal side subtend equal angles).
Angle AOC = 180 -(60+60) =60 .
Therefore Triangle AOC is equilateral triangle.

Now that we established Triangle AOC is equilateral, we now require only one parameter to answer any question related to the diagram. And that parameter is radius. Explore the statements which gives you radius value

Statement-1 : Here it is stated difference between arc lengths is 16*pie

We know length of arc formula, using that we can find radius. So statement-1 is sufficient

Statment-2 : Gave us area of triangle. We know area of triangle formula, using that formula we determine length of side which nothing but radius of circle. So statement-2 is also Sufficient

Hence Option "D" is the answer.
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1. The length of arc CDA is 16π greater than the length of arc ABC.

Notice that this is an equilateral triangle. So the length of the arc ABC is 60/360 = 1/6. And the rest is 5/6 (300 degrees)

Set the circumference equal to each other

2πr(5/6)=2πr(1/6)+16π (because the entire thing equates to the total diameter)

pies cancel out. Solve for R which is 12.
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Hello from the GMAT Club BumpBot!

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