Question

Square ABCD is inscribed in circle 0. What is the area of square region ABCD ?
(1) The area of circular region 0 is 647$\pi$.
(2) The circumference of circle 0 is 167$\pi$.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

Since the area of square ABCD is the square of its side length, to solve this problem it is necessary to determine the side length of ABCD. From the figure, a diameter of the circle coincides with a diagonal of the square. If the length of a diameter of the circle can be determined, then the length of a diagonal of the square can be determined, from which the side length of the square can be determined using the Pythagorean theorem.