If O is the center of the circle above and the length of chord AB is 2

From the question , we can see a triangle inscribed in a circle where 2 legs are the radius. This tells us that it's an isoceles triangle

The length of chord AB is 2 meaning we can divide the triangle into two equal right angles triangle with a base measurement of 1cm on each side.

Statement 1- The area of ΔOAB is root 3 square units:

From the area of the triangle 1/2 *b*h, we can deduce the height of the triangle to be root 3, since we have already established earlier that the base is 1cm .

Going by this, we know we are dealing with a 30-60-90 triangle, and we can figure out that the angle AOB is 60 degrees, and that the radius is 2 square units ..

Hence we can find the length of Arc ------------》 sufficient


Statement 2. The area of sector OACBO is 2pi/3

because we don't know the radius of the circle, we cannot find the angle AOB.
We're left with 2 unknowns... both the radius and the angle SON, hence we cannot deduce the length of Arc
Statement 2 ----》insufficient

The answer is A.

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Is it not theoretically possible to calculate the angle subtended by the arc from statement 2? Since I know the length of the chord AB, I can derive a relationship between the radius and the angle of the arc/2.

Can any expert suggest?

Yes this can be true. we have two equations one with the fact that area is given and other being the chord length.