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04 Jul 2010, 14:56
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
83% (02:48) correct
17%
(02:44)
wrong
based on 6
sessions
History
Date
Time
Result
Not Attempted Yet
Please explain.
If a circle passes through points \((1, 2)\) , \((2, 5)\) , and \((5, 4)\) , what is the diameter of the circle?
(C) 2008 GMAT Club - [t]s12#10[/t]
* \(\sqrt{18}\)
* \(\sqrt{20}\)
* \(\sqrt{22}\)
* \(\sqrt{26}\)
* \(\sqrt{30}\)
If a circle passes through points \((1, 2)\) , \((2, 5)\) , and \((5, 4)\) , what is the diameter of the circle?
(C) 2008 GMAT Club - [t]s12#10[/t]
* \(\sqrt{18}\)
* \(\sqrt{20}\)
* \(\sqrt{22}\)
* \(\sqrt{26}\)
* \(\sqrt{30}\)
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04 Jul 2010, 15:18
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appy001
seems this question has been discussed exhaustively in a previous thread. To avoid multiplicity of same topic,
I'd advise that you do a search.
However, OA is B because the two points (1,2) & (5,4) are at the end-points of the diameter.
Check: slope of the said points from (2, 5) are perpendicular to each other i.e their products = -1.
05 Jul 2010, 03:01
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gmatbull
Just to elaborate more on this...
Slope of line connecting points (1,2) and (2,5) is 3
Slope of line connecting points (2,5) and (5,4) is -1/3
We know that if two lines are perpendicular then their slope will be negative reciprocal of each other. So the above 2 lines are perpendicular.
We also know that if three points on a circle form a right angle then two of the points will be form the diameter. So here line connecting (1,2) and (5,4) will be the diameter as the right angle is at (2,5)
So the length of the diameter of the circle is: Sqrt(16+4)=sqrt(20)--Ans(B)
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 Problem Solving (PS) 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!
