Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
In the figure above, a shaded circle with diameter is tangent to a large semicircle with diameter at points and . Point is the center of the semicircle, and is perpendicular to . If the area of the large semicircle is , what is the area of the shaded circle?
The Correct answer is C.
Explanation
Segment is a radius of the large semicircle, and it is also a diameter of the shaded circle, so the radius of the large semicircle is equal to twice the radius of the shaded circle. Let be the radius of the shaded circle. Then is the radius of the large semicircle, and so the area of the semicircle is . This area is given as , and so the area of the shaded circle is .