Multiple choice

Direction: The following question has two statements, (1) and (2). Answer the question using the following options: A parallelogram is inscribed in a circle. What is the perimeter of the parallelogram? (1) One side of the parallelogram is 5 cm. (2) The area of the circle is 169 π cm2.

  1. if statement (1) alone is sufficient but statement (2) alone is not

  2. if statement (2) alone is sufficient but statement (1) alone is not

  3. if both (1) and (2) together are sufficient but none of them alone is sufficient

  4. if both statements are sufficient independently

  5. if both (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A parallelogram inscribed in a circle must be a rectangle. The diagonal of the rectangle is the diameter of the circle. Statement (2) gives the area of the circle (pi * r^2 = 169 * pi), so r = 13, diameter = 26. With one side = 5, the other side is sqrt(26^2 - 5^2) = sqrt(676 - 25) = sqrt(651). Perimeter = 2 * (5 + sqrt(651)). Both statements are required.

AI explanation

A parallelogram has opposite angles equal, and if it is inscribed in a circle, its opposite angles must sum to 180 degrees, proving it is a rectangle. Statement one gives one side as 5 cm, and statement two gives the circle's area as 169 pi, meaning its radius is 13 cm and the diagonal of the rectangle is the diameter, 26 cm. Using the Pythagorean theorem with both statements, the other side of the rectangle is the square root of 26 squared minus 5 squared = 25 cm, so both statements together are sufficient to find the perimeter of 2 times 5 plus 2 times 25, while neither alone is enough.

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