The answer is C.
Beginning with the second peice of evidence we can deduce that line AB is, in fact, the diameter, which is important because the question stem does not tell us that AB is the diameter. It also tells us that the measurement of ACB is 90, which makes this a right triange. This does not allow us to derive the area though so (2) is insufficient.
(1) On its own right is insufficient because it only gives us only one of the angle measurements. Some people might look at the triangle and assume it is a right triangle and begin making the deductions below, but again, we don't know that this is a right triangle from (1) information alone.
Putting (1) and (2) together we know the triangle is a 30-60-90 right triangle. 30-60-90 right triangles have definite ratios for the lengths of their sides. From smallest side to largest side the ratio is x : x[sqrt(3)] : 2x. Thus, if the largest AB is the diameter and 18, then the smallest side (or base in this example) would be equal to 9 (18/2) and the largest second longest side would be 9[sqrt(3)]. Thus, you know the base and the height and can multiply them together and devide by two to get the area (bh/2). Thus, C is the answer.
