Statement 1:
AB = 18, angle ABC = 30 degree

We need three parameter to fix a triangle.

Insufficient

Statement 2:
2 * pie * r = 18 * pie
r = 9
AB is diameter and angle ACB = 90 degree

Still multiple triangle can be formed.

Insufficient

Statement 1 and 2:
AB = 18, angle ABC = 30 degree, angle ACB = 90 degree

Now, we can find area.

Sufficient

Answer: C

so then my question is, so then are we assuming that sine can not be used. If we can use sine then the 30 deg is all we need.

Angle ACB = 90 degree is not given in question. We can get it from statement 2 only.

Area of triangle = 1/2 ab sinC = 1/2 bc sinA = 1/2 ca sinB

We need three parameter to fix a triangle if all sides are different.

I believe that this much is enough to understand.

akhp77 wrote:Angle ACB = 90 degree is not given in question. We can get it from statement 2 only.

Area of triangle = 1/2 ab sinC = 1/2 bc sinA = 1/2 ca sinB

We need three parameter to fix a triangle if all sides are different.

I believe that this much is enough to understand.

I have a question about this though....from the picture...its pretty clear to me that line segment AB is the diameter of the circle. Is it not true that if a triangle can be inscribed within a circle, and one of its sides is the diameter of the circle, the triangle must be a right triangle? If that is the case, from A we know that the triangle is a 30-60-90 triangle. The sides of these triangles have a ratio of 1:2:sqrt(3)......therefore we can get the sides of the triangle and find the area. If so...I would say A is the answer....B is stated in the stem...Please let me know.

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.

Stem: The diagram tries to make it appear that AB is diameter but keep in mind that we have no info as such stating whether AB is the diameter
We just know AB=18


(1) We have no idea about rest of angles or sides. Clearly Insuff

(2)
Since 2*pi*r=18
2r=d=18
But AB =18
Hence AB=diameter
This implies ACB is 90, but we have no info about other sides or angles hence Insuff

(combined)
We know ACB = 90 , ABC = 30 hence CAB = 30
30-60-90 is 1 - 2 - root3 and we know one side so we can find base and height and hence area
Suff

Answer C