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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:37) correct
0% (00:00) wrong based on 2 sessions
History
Date
Time
Result
Not Attempted Yet
O is the center of the circle above.
Quantity A
x
Quantity B
5
GMAT-Club-Forum-7jj4n3n6.jpeg [ 45 KiB | Viewed 543 times ]
O is the center of the circle above.
Quantity A
x
Quantity B
5
Attachment:
GMAT-Club-Forum-7jj4n3n6.jpeg [ 45 KiB | Viewed 543 times ]
22 Jun 2024, 01:57
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If you put the stem O, which is the center of the circle above, into the image and take a screenshot, then the question is difficult to find out.
The image of the circle above should not contain the stem, as per the original question
Please, be more careful when you post a question.
Thank you
The image of the circle above should not contain the stem, as per the original question
Please, be more careful when you post a question.
Thank you
13 Jul 2024, 11:54
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Official Explanation
In this question you are asked to compare x with 5, where x is the length of a line segment from the center of the circle to a point inside the circle. In a circle the easiest line segments to deal with are the radius and the diameter. Looking at the figure in the question, you can see that you can draw two radii, each of which “completes” a right triangle, as shown in the figure below.
Since in one of the triangles the lengths of both legs are known, you can use that triangle to determine the length of the radius of the circle. The triangle has legs of length 3 and 4. If the length of the radius is r, then, using the Pythagorean theorem, you can see that
\(r^2=3^2+4^2\) or
\(r^2 = 9+16\) or
\(r^2 = 25\) and thus, r=5
Since the length of the radius of the circle is 5 and the line segment of length x is clearly shorter than the radius, you know that x<5, and the correct answer is Choice B.
You could also see that the two triangles are congruent, and so x = 4, again yielding Choice B.
In this question you are asked to compare x with 5, where x is the length of a line segment from the center of the circle to a point inside the circle. In a circle the easiest line segments to deal with are the radius and the diameter. Looking at the figure in the question, you can see that you can draw two radii, each of which “completes” a right triangle, as shown in the figure below.
Since in one of the triangles the lengths of both legs are known, you can use that triangle to determine the length of the radius of the circle. The triangle has legs of length 3 and 4. If the length of the radius is r, then, using the Pythagorean theorem, you can see that
\(r^2=3^2+4^2\) or
\(r^2 = 9+16\) or
\(r^2 = 25\) and thus, r=5
Since the length of the radius of the circle is 5 and the line segment of length x is clearly shorter than the radius, you know that x<5, and the correct answer is Choice B.
You could also see that the two triangles are congruent, and so x = 4, again yielding Choice B.
Attachment:
GMAT-Club-Forum-hjvne24x.jpeg [ 21.92 KiB | Viewed 523 times ]
