1986 AJHSME Problems/Problem 23
The large circle has diameter . The two small circles have their centers on and just touch at , the center of the large circle. If each small circle has radius , what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
The small circle has radius , thus its area is . The large circle has radius , thus its area is . The area of the semicircle above is then . The part that is not shaded are two small semicircles. Together, these form one small circle, hence their total area is . This means that the area of the shaded part is . This is equal to the area of a small circle, hence the correct answer is .