Square ABCD is inscribed in circle O. What is the area of square region ABCD?

[BTGmoderatorDC]

Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.



OA D

Source: Official Guide

[Jay@ManhattanReview]

Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.

OA D

Source: Official Guide

Let's take each statement one by one.

(1) The area of circular region O is 64π.

=> πr^2 = 64π => r = 8; where r = radius of the circle

Thus, the diameter of the circle = 16;
Side of the square = 16/√2
Area of the square = side^2 = (16/√2)^2 = 128. Sufficient.

(2) The circumference of circle O is 16π.

=> 2πr = 16π => r = 8

This is the same information that we got in Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.



OA D

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the area of square region ABCD, which is inscribed in circle O. Recall that the diameter of a circle is the diagonal of its inscribed square. Therefore, if we can determine the radius (and hence the diameter) of the circle, then we can determine the diagonal (and hence the side and area) of the inscribed square.

Statement One Alone:

Since we are given the area of the circle, we can determine its radius, and hence we can determine the area of the inscribed square. Statement one alone is sufficient.

Statement Two Alone:

Since we are given the circumference of the circle, we can determine its radius, and hence we can determine the area of the inscribed square. Statement two alone is sufficient.

Answer: D