Concept: The question tests on the area of Geometry(DS).

Statement 1: OAB is an isosceles triangle and A lies inside the circle

This statement means that OA, can be the unequal side. In this case then OB and AB are the equal sides and point B, can lie inside or outside the circle.

. Answer options could be B, C or E. Statement 1 is insufficient

Statement 2: OAB is an equilateral triangle and A lies inside the circle.

This means that OA = OB = AB, and if A lies in the circle, then B also has to lie within the circle.

Statement 2 is sufficient.
 (Option B)