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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] 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.
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Re: If A and C are points in a plane, C is the center of circle [#permalink] 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] New post 28 May 2012, 02:49
Expert's post
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] 28 May 2012, 02:49
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If A and C are points in a plane, C is the center of circle

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