Nova geometry D.S set c - q 17

Nidhs wrote:An equilateral triangle is inscribed inside a circle. what is the area of the triangle?
1) The radius of the circle is 2
2) The ratios of the radius of the circle to a side of the triangle is 1:3

The answer is a. Could someone ls explain to me the soln?

For every circle, there's only one size equilateral triangle that can possibly be inscribed within.

So, if we know the radius of the circle, it has to be possible to figure out the area of the triangle. One of the nice things about DS is that even if we have no clue how to do the calculation, we know there has to be some way to do so: statement (1) is sufficient.

Just knowing the ratio of the radius to a side doesn't help, since we don't have any actual measurements.

(1) is sufficient and (2) is insufficient: choose A.

Equilateral triangles are 60 degrees for each angle, say triangle ABC

and since it's inscribed inside a circle, then the corresponding angles AOB, AOC, and BOC are 60*2=120 where O is the centre of the circle, and these triangles are isosoles trangles with sides r. Knowing one of the angles and the length of the 2 sides would allow us to find the length of the 3rd side AB, AC, BC, and thus the area of the angle can be calculated.

But, would we ever be tested on the GMAT to find something like this?
The formula to calculate the 3rd side given 2 sides and an angle is pretty complicated from what I can remember.