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08 May 2008, 10:13
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I ran across this question and think the answer provided is incorrect.
Sorry this image is so huge! (If anyone can help me shrink it, that'd be great.)
See the bottom of the page for the image, I'll post the question and info regarding the image as this image is not identical to the one in the quesiton.
**IMAGE NOTES**
The square is inside the circle. The corners of the square are points labeled A, B, C, and D on the circle. A=Top Left, B=Top Right, C = Bottom Right, D = Bottom Left. B & D are identified as right angles. A line connects AC. There is no center of the circle indicated. Here is the question:
**QUESTION**
If points A, B, C, and D are points on the circumference of the circle in the figure [below], what is the area of ABCD?
1) The radius of the circlie is \(\frac{\sqrt{2}}{2}\)
2) ABCD is a square.
**END QUESTION**
I was thinking the answer is A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient. (Note: while typing this, I realize that the answer is C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient, which was the answer given.)
Here is my reasoning:
When you know the radius of the circle, you also know the length of segment AC because AC is also the diameter of the circule. You're asked to find the area of the quadralateral ABCD. Using \(a^2 + b^2 = c^2\) doesn't quite get you all the way there. We don't know if it's a special traingle (i.e., \(1-1-sqrt{2}\)). If we did (i.e. a square), then we could figure the area of triangle and double it for the area of ABCD.
Double the radius, so \(2 * \frac{\sqrt{2}}{2}=\sqrt{2}\)[diameter of circle]. So if the hypotnuse of the triangle is \(\sqrt{2}\), then this is a special triangle, and know the base is 1, height = 1, so the area of the square is 1.
If ABCD is a non-square, we still only have the hypotnuse (sp?) of the triangle. We need 2 of 3 for the \(a^2 + b^2 = c^2\) to work. BOTH together are sufficient once we know that ABCD is a square and can use \(1-1-sqrt{2}\).
Even though I answered my own question while writing it, I hope this helps others.
Sorry this image is so huge! (If anyone can help me shrink it, that'd be great.)
See the bottom of the page for the image, I'll post the question and info regarding the image as this image is not identical to the one in the quesiton.
**IMAGE NOTES**
The square is inside the circle. The corners of the square are points labeled A, B, C, and D on the circle. A=Top Left, B=Top Right, C = Bottom Right, D = Bottom Left. B & D are identified as right angles. A line connects AC. There is no center of the circle indicated. Here is the question:
**QUESTION**
If points A, B, C, and D are points on the circumference of the circle in the figure [below], what is the area of ABCD?
1) The radius of the circlie is \(\frac{\sqrt{2}}{2}\)
2) ABCD is a square.
**END QUESTION**
I was thinking the answer is A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient. (Note: while typing this, I realize that the answer is C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient, which was the answer given.)
Here is my reasoning:
When you know the radius of the circle, you also know the length of segment AC because AC is also the diameter of the circule. You're asked to find the area of the quadralateral ABCD. Using \(a^2 + b^2 = c^2\) doesn't quite get you all the way there. We don't know if it's a special traingle (i.e., \(1-1-sqrt{2}\)). If we did (i.e. a square), then we could figure the area of triangle and double it for the area of ABCD.
Double the radius, so \(2 * \frac{\sqrt{2}}{2}=\sqrt{2}\)[diameter of circle]. So if the hypotnuse of the triangle is \(\sqrt{2}\), then this is a special triangle, and know the base is 1, height = 1, so the area of the square is 1.
If ABCD is a non-square, we still only have the hypotnuse (sp?) of the triangle. We need 2 of 3 for the \(a^2 + b^2 = c^2\) to work. BOTH together are sufficient once we know that ABCD is a square and can use \(1-1-sqrt{2}\).
Even though I answered my own question while writing it, I hope this helps others.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
09 May 2008, 10:09
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I think C is the right answer. In the question he said A,B,C and D are points on a circle. Consider two points A and B are the points of the diameter of the circle and B and C lie on the same side.I guess we cannot solve for area using statement 1
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
