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19 Nov 2010, 04:33
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
47% (01:53) correct
53%
(02:05)
wrong
based on 377
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Is the radius of the circle greater than 3?
(1) (2,4) and (5,10) lie on the circle.
(2) (2,4) and (4,1) lie on the circle.
My understanding is that the question asks us whether the radius of the circle greater than 3 or not? Thus if we are able to get a Yes or No from the option, it should suffice.
(1) (2,4) and (5,10) lie on the circle.
(2) (2,4) and (4,1) lie on the circle.
My understanding is that the question asks us whether the radius of the circle greater than 3 or not? Thus if we are able to get a Yes or No from the option, it should suffice.
19 Nov 2010, 04:55
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gdk800
Yes, your understanding is correct.
Maximum distance between two points on a circle is the length of its diameter (so when these points are the endpoints of a diameter), so the max distance = diameter = 2 radii.
So for example if we are told that the distance between the two points on a circle is 10cm then we can be sure that the diameter is more than or equal to 10 (or the radius is more than or equal to 10/2=5).
Next, the formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).
Now, back to the original question:
Is the radius of the circle greater than 3?
1) (2,4) and (5,10) lie on the circle --> the distance between these points is \(d=\sqrt{(2-5)^2+(4-10)^2}=\sqrt{45}>6\), so the diameter of this circle must be more than 6, thus the radius must be more than 3 --> answer to the question is YES. Sufficient.
2) (2,4) and (4,1) lie on the circle --> the distance between these points is \(d=\sqrt{(2-4)^2+(4-1)^2}=\sqrt{13}<6\), so the diameter of this circle may or may not be more than 6. Not sufficient.
Answer: A.
14 Aug 2012, 07:38
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conty911
Any side of a triangle is less than or equal to the diameter of the circumscribed circle. The diameter is the largest chord in any circle.
Only for right angled triangles, one of the sides is equal to the diameter, specifically the hypotenuse.
The question asks whether the diameter is greater than 6.
(1) The distance between the two points is \(\sqrt{(5-2)^2+(10-4)^2}=\sqrt{9+36}>6.\)
Sufficient.
(2) The distance between the given two points is \(\sqrt{(4-1)^2+(2-4)^2}=\sqrt{9+4}<6.\)
Since through two points there are infinitely many circles passing through, some of them will have diameter greater than 6, others won't.
Not sufficient.
Answer A
