From the stem you can't really conclude what the triange looks like but we do know the absolute longest any side of the triangle can be is the diameter of the circle.
1) this tells us that the radius is 4 and one side of the triangle is the diameter. Thus, that side must be the longest side and the other two sides will form a right triangle. You can see that the circumference would be 8(pi) - since pi is greater than three the question is whether the other sides of the triangle can be greater than 8. They cannot thus we know that the permieter of the triangle will always be smaller. Sufficient.
2) Equilateral triangle is an invitation to a 30:60:90 - you just have to find it. Draw a circle with an equilateral triangle inside and then draw a line from each point of the triangle to the center of the circle. each of these lines are radii and the central angle created is 120. Thus you know the other angles are 30 - there is your 30:60:90 - draw a right angle from the 120 to create this. The ratio of sides in this type of triangle is a:a(rt3):2a - since the radius is opposite the 90 angle you know that r = 2a - thus the side opposite the 60 is r/2(rt3). This is one half of a side of the equilateral. Therefore the side of the equilateral is r(rt3). and the perimeter is
r(rt3)(3). now we have to compare that to the circumference which is 2r(pi). we know that pi is bigger than 3 and 2 is larger than rt3 - therefore the perimeter of the circle will always be greater and the answer is D.
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