SAT Math Multiple Choice Question 702: Answer and Explanation
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.