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M23 q 27 [#permalink] New post 20 Mar 2012, 13:58
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The center of the circle is at point (0, 6) . If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?


* 36\pi
* 45\pi
* 64\pi
* 81\pi
* 100\pi



Can someone please explain this question stem with figure?
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Re: M23 q 27 [#permalink] New post 20 Mar 2012, 14:10
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I'm ecstatic that I got this!

WOOOOOOOOTTTTTTTTTTT!

Anyhow after that bit of superfluous celebration - here is how i get it:

Since the distance between 2 points that intersect the X-axis is 16... Thus the 2 points on x axis are (0,-8) & (0,8)

So we have a point on the circle and the center (6,0)

Using distance formula the radius = \sqrt{((8-0)^2+(6-0)^2)}=10

Thus circle area = pi * r^2 = 100Pi
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Re: M23 q 27 [#permalink] New post 20 Mar 2012, 14:21
teal wrote:
The center of the circle is at point (0, 6) . If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?


* 36\pi
* 45\pi
* 64\pi
* 81\pi
* 100\pi



Can someone please explain this question stem with figure?


Below is a diagram:
Attachment:
Circle.png
Circle.png [ 11.15 KiB | Viewed 535 times ]
As you can see the radius of the circle is a hypotenuse of a right triangle with the sides equal to 6 and 16/2=8 (6-8-10 right triangle), so radius=hypotenuse=10. The area is \pi{r^2}=100\pi.

Answer: E.

Hope it helps.
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Re: M23 q 27 [#permalink] New post 09 Apr 2012, 19:35
Thank you...makes sense!
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The center of the circle is at point (0, 6)[/m]. If the [#permalink] New post 13 Dec 2012, 03:01
The center of the circle is at point (0, 6). If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A. 36\pi
B. 45\pi
C. 64\pi
D. 81\pi
E. 100\pi

Last edited by Bunuel on 13 Dec 2012, 03:05, edited 1 time in total.
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Re: The center of the circle is at point (0, 6)[/m]. If the [#permalink] New post 13 Dec 2012, 03:09
arnijon90 wrote:
The center of the circle is at point (0, 6). If the distance between the two points where the circle intersects the x-axis is 16, what is the area of the circle?

A. 36\pi
B. 45\pi
C. 64\pi
D. 81\pi
E. 100\pi


Merging similar topics. Please refer to the solutions above.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: The center of the circle is at point (0, 6)[/m]. If the   [#permalink] 13 Dec 2012, 03:09
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