SAT Math Multiple Choice Practice Question 608: Answer and Explanation

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Question: 608

22. What is the area of a circle centered at (4, 3) that passes through the origin?

A. 9π
B. 12π
C. 16π
D. 25π
E. 49π

Correct Answer: D


D Whenever a question describes a geometric figure but doesn't show it, draw it out. The center is at (4, 3), and the circle passes through the origin. The key to any circle is knowing the radius, which in this case is a line between the center at (4, 3) and the origin, as shown in the following diagram:

This makes it clear that the radius is the hypotenuse of a right triangle that has legs of 3 and 4. You can use the Pythagorean theorem or remember that 3:4:5 is a Pythagorean triplet. Since the radius has length 5, Area = πr2 = π52 = 25π, answer D.