SAT Math Multiple Choice Practice Question 48: Answer and Explanation

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Question: 48


In this circle, point O is the center of the large circle, and points P and Q are the centers of the two smaller circles. If the distance PQ = 6, then the area of the large circle is

A. 144π
B. 72π
C. 36π
D. 12π
E. 6π

Correct Answer: C


C. The key to figuring out this problem is noticing that the line containing points O, P, and Q is a diameter of the large circle and that it also contains the diameters of the two smaller circles. So the diameter of circle O equals the sum of the diameters of circles P and Q. Meanwhile, the line segment PQ is composed of the radii (plural of radius) of the two small circles. Because these two radii add up to 6, the diameters of the small circles add up to 12. The diameter of circle O is 12 and its radius is 6. Finally, because the circle's area is πr2, the large circle's area is π(6)2 = 36π.

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