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M23 q 27

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M23 q 27 [#permalink] New post 20 Mar 2012, 12:58
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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, 13:10
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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, 13:21
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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 1379 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, 18:35
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, 02:01
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, 02:05, 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, 02:09
Expert's post
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.
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Re: M23 q 27 [#permalink] New post 04 Mar 2014, 09:20
Oh tought question !

I hate when question wants us to make a figure ! GMAT test makers shud spent some time to make figure for us ! :P

I chose A.

how can one assume circle will touch -4? and 16? that was the difficult to do in this question.
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Re: M23 q 27 [#permalink] New post 04 Mar 2014, 09:29
Expert's post
sanjoo wrote:
Oh tought question !

I hate when question wants us to make a figure ! GMAT test makers shud spent some time to make figure for us ! :P

I chose A.

how can one assume circle will touch -4? and 16? that was the difficult to do in this question.


Circle does not cross x-axis at -4 and 16. It crosses x-axis at -8 and 8. Check here: m23-q-129402.html#p1062068

Hope it helps.
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COLLECTION OF QUESTIONS:
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Re: M23 q 27 [#permalink] New post 05 Mar 2014, 03:03
Bunuel wrote:
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
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.


M taking abt y intercept which is 16 and x intercept -4?How did u draw this !
I understood that it will cross 8 and -8 on both side of x axis.
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Re: M23 q 27 [#permalink] New post 05 Mar 2014, 04:28
Expert's post
sanjoo wrote:
Bunuel wrote:
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
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.


M taking abt y intercept which is 16 and x intercept -4?How did u draw this !
I understood that it will cross 8 and -8 on both side of x axis.


Sorry but do not follow you. What do you mean by "how did you draw it"?

If you understand that x intercepts are at -8 and 8, then you can get the radius as shown in my post. Drawing is just to illustrate.
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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. ,11 Mixed Questions, 12 Fresh Meat

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Re: M23 q 27 [#permalink] New post 05 Mar 2014, 06:34
Ohk Bunuel dear .. Finally I got that now.. hypotenuse is 10 so from 6 to -4 distance is 10 and from 6 to 16 distance is 10..Its clear now
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Re: M23 q 27 [#permalink] New post 06 Jul 2014, 12:32
How will I understand without drawing that the two points are (0, -8) and (0, 8)? Why not (0, -7) and (0, 9)? Please make it clear.
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Re: M23 q 27 [#permalink] New post 06 Jul 2014, 12:37
Expert's post
Raihanuddin wrote:
How will I understand without drawing that the two points are (0, -8) and (0, 8)? Why not (0, -7) and (0, 9)? Please make it clear.


The center of the circle is on y-axis, so it's symmetric around it. We know that the the distance between the two points where the circle intersects the x-axis is 16, hence half of it (8 units) must be to the left of 0 and the remaining half (another 8 units) to the right of 0.

Does this make sense?
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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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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Re: M23 q 27   [#permalink] 06 Jul 2014, 12:37
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