SAT Math Multiple Choice Practice Question 152: Answer and Explanation
In the figure above, OAC is one quarter of a circle with a radius of 8. If AB = OC, then the area of the shaded region is
Correct Answer: A
A. Because AB = OC, it's also true that AB = OA and AB = OB (because OA and OB are also radii, and all radii are equal). That makes OAB an equilateral triangle, so all of its angles equal 60°. Therefore, angle BOD must be 30°, which makes triangle BOD a 30-60-90 triangle. Using the 30-60-90 pattern (which is at the top of the math section, if you forget it), you know that BD = 4 and OD = and that the area of triangle BOD is . Now the shaded region equals the circular sector BOC minus triangle BOD, and sector BOC is one-twelfth of a circle (because it has 30° out of the 360° in a circle). So the area of BOC is . After all that work, you discover the right answer is Choice (A).