Data sufficiency: Find the area of the shaded region

[mjfsutherland]

I have a Data sufficiency question related to a gmat prep question from the "Learning Express's GMAT exam success" study book.

The Question is

Find the area of the shaded region.

The diagram shows a circle containing a triangle. Points A and B lie on the circle and the line segment joining them pass through point D at the centre of the circle. Point C also lies on the circle. The triangle is ABC. The shaded region is the area of the circle minus the area of the triangle.

1) Angle A is 43 degrees
2) AB is 10cm

OA = E

Official Explanation is:

Statement (1) is not sufficient. The fact that angle A is 43 degrees does not give you enough information about the rest of the triangle or the circle. Statement (2) is also not sufficient. Even though the diameter, or AD [this seems to be a mistake as well as the diameter should be AB not AD], equals 10, you cannot assume that this is the altitude or height of the triangle.

The answer I gave was C because a triangle situated in a semi circle will always have a 90 degree angle opposite the side sitting on the diameter of the circle. If the triangle is a right triangle and you know the hypotenuse and you know one of the angles then you can figure out the area of the triangle. You also know the area of the circle as you were given the diameter, therefore you can calculate the shaded region, given both pieces of data.

Can someone tell me if my reasoning is sound. My only doubt is that diagrams in gmat exams are never drawn accurately so perhaps we cant assume that points A, B and C actually lie on the circle as they appear to?

[esledge]

I think your reasoning is sound and the answer is C, interpreting C loosely as "it is theoretically possible to answer with both statements."

My one concern is that to actually calculate the area, you'd need trigonometry to find the exact height of the triangle. It would be different if the given angle were 30,45, or 60, and we could use common triangle side ratios, the closest the GMAT comes to trig.

So that's probably why the official answer was listed as E, but I think the GMAT steers clear of "E only because you can't use trig on the GMAT" answers.