mg188 wrote:
Hi, I think B should be the correct answer. AB is the diameter and angle ACB is a right-angle triangle (a triangle drawn in a semi-circle is a right-angled triangle).
If we draw a perpendicular line from vertex C to line AB, the line would be the radius of the circle (also the height of the triangle).
We can apply the 1/2 x Base x Height to get the area as = 1/2 x 18 x 9 = 81 units
Bunuel, what's the error in this?
Hi mg188,
The information in Fact 2 does help us prove that AB is the diameter of the circle (and thus, the radius is equal to 9). However, we still have NO idea where Point C is on the circumference.
IF... Point C is exactly in the 'middle' of the circumference between Point A and Point B, then we would have a 45/45/90 right triangle and we could calculate the area of that triangle (as there would be just one variable to solve for in the equation X^2 + X^2 = 18^2; in this situation, you could draw a radius from point C to the center - and you would have the 'height', assuming you set the 'base' as the diameter). However, if Point C is anywhere else on the circumference, then we do NOT have a 45/45/90 right triangle (we end up with some other right triangle in which the two legs are DIFFERENT lengths) - and we end up with one equation and two variables: X^2 + Y^2 = 18^2, meaning that we cannot calculate a definitive area for the triangle. Drawing that additional radius here would NOT equal the 'height' of the triangle, since we would not be forming a 90-degree angle with the circumference. This is ultimately why Fact 2 is Insufficient on its own.
GMAT assassins aren't born, they're made,
Rich
Contact Rich at: Rich.C@empowergmat.com