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 
.
