SAT Math Multiple Choice Question 702: Answer and Explanation

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Question: 702

12. Images

Note: Figure not drawn to scale.

In the figure above, rectangle ABCD is inscribed in the circle with center O. What is the area of the circle?

  • A. 26π
  • B. 121π
  • C. 144π
  • D. 169π

Correct Answer: D



Special Topics (circles) MEDIUM


Since ABCD is a rectangle, we can find the length of its diagonal using the Pythagorean Theorem: 102 + 242 = d2. Even better, we can notice that the two legs are in a 5:12 ratio, and therefore triangle BCD is a 5-12-13 triangle. In either case, we find that DB = 26. Since DB is also a diameter of the circle, the radius of the circle is 26/2 = 13, and therefore, the area of the circle is πr2 = π(13)2 = 169π.

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