Important: AC is the DIAMETER of the circle.
Since ∠ABC holds (or contains) the DIAMETER, ∠ABC = 90 degrees.
So, we have a RIGHT TRIANGLE.
Side AC is the HYPOTENUSE and it has length 2
Side BC is a leg and it has length 1
To find the missing side, we'll us the Pythagorean Theorem:
1² + (side AB)² = 2²
1 + (side AB)² = 4
So, (side AB)² = 3
So, side AB = √3
Since we have a RIGHT TRIANGLE, the area = (1/2)(base)(height)
If we let side AB be the base, then side BC is the height.
So, the area = (1/2)(√3)(1)
= [spoiler]√3/2[/spoiler]
=
B
RELATED RESOURCE
See this video to learn all of the circle properties that the GMAT tests:
https://www.gmatprepnow.com/module/gmat ... /video/880
Cheers,
Brent