If A and C are points in a plane, C is the center of circle : GMAT Data Sufficiency (DS)
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If A and C are points in a plane, C is the center of circle

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If A and C are points in a plane, C is the center of circle [#permalink]

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New post 27 May 2012, 08:36
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If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

(1) The circumference of circle O is xπ.
(2) The area of circle O is xπ.
[Reveal] Spoiler: OA
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Re: If A and C are points in a plane, C is the center of circle [#permalink]

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New post 27 May 2012, 18:01
Perimeter of circle is 2*pi*r. From first statement we can find out that x is the diameter of circle so point A has to be outside of the circle.

Answer is A.
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Re: If A and C are points in a plane, C is the center of circle [#permalink]

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If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

Notice that point A will be outside the circle if the radius of the circle is less than x (the distance between the center of the circle and point A). So, the question basically asks whether \(r<x\).

(1) The circumference of circle O is xπ --> \(2\pi{r}=x\pi\) --> \(2r=x\) --> \(x>r\). Sufficient.
(2) The area of circle O is xπ --> \(\pi{r^2}=x\pi\) --> \(x=r^2\). If \(x=4\) and \(r=2\) then the answer is YES but if \(x=\frac{1}{4}\) and \(r=\frac{1}{2}\) then the answer is NO. Not sufficient.

Answer: A.
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Re: If A and C are points in a plane, C is the center of circle [#permalink]

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Re: If A and C are points in a plane, C is the center of circle [#permalink]

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New post 14 Jul 2016, 02:15
Hello from the GMAT Club BumpBot!

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Re: If A and C are points in a plane, C is the center of circle [#permalink]

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New post 24 Jul 2016, 05:03
macjas wrote:
If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

(1) The circumference of circle O is xπ.
(2) The area of circle O is xπ.

(1) 2πr=xπ
2r=x-----Dia of circle.
if c is centre and AC=x then point A must lie outside of circle.
(2)πr^2=xπ
r^2=x
x=2 it means AC=2 and radius of circle is Sq.root2 then A may lie inside or outside the circle since dia. of circle is 2*sq.root2....insuff...
Ans A
Re: If A and C are points in a plane, C is the center of circle   [#permalink] 24 Jul 2016, 05:03
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