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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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27 May 2012, 09:36
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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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27 May 2012, 19:01
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.

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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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28 May 2012, 03:49
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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.

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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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06 Jan 2015, 04:51
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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14 Jul 2016, 03:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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24 Jul 2016, 06:03
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, 06:03
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