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# M23 q 27

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Manager
Joined: 13 May 2010
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M23 q 27 [#permalink]

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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?

Kudos [?]: 24 [0], given: 4

Manager
Joined: 22 Feb 2012
Posts: 93

Kudos [?]: 27 [1], given: 25

Schools: HBS '16
GMAT 1: 740 Q49 V42
GMAT 2: 670 Q42 V40
GPA: 3.47
WE: Corporate Finance (Aerospace and Defense)
Re: M23 q 27 [#permalink]

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20 Mar 2012, 14:10
1
KUDOS
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

Kudos [?]: 27 [1], given: 25

Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 135216 [1], given: 12673

Re: M23 q 27 [#permalink]

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20 Mar 2012, 14:21
1
KUDOS
Expert's post
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 [ 11.15 KiB | Viewed 2812 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 $$\pi{r^2}=100\pi$$.

Hope it helps.
_________________

Kudos [?]: 135216 [1], given: 12673

Manager
Joined: 13 May 2010
Posts: 122

Kudos [?]: 24 [0], given: 4

Re: M23 q 27 [#permalink]

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09 Apr 2012, 19:35
Thank you...makes sense!

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Intern
Joined: 18 Mar 2012
Posts: 13

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The center of the circle is at point (0, 6)[/m]. If the [#permalink]

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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.

Kudos [?]: 6 [0], given: 3

Math Expert
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Kudos [?]: 135216 [0], given: 12673

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

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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.
_________________

Kudos [?]: 135216 [0], given: 12673

Senior Manager
Joined: 06 Aug 2011
Posts: 386

Kudos [?]: 239 [0], given: 82

Re: M23 q 27 [#permalink]

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04 Mar 2014, 10:20
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 !

I chose A.

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

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Kudos [?]: 239 [0], given: 82

Math Expert
Joined: 02 Sep 2009
Posts: 42543

Kudos [?]: 135216 [0], given: 12673

Re: M23 q 27 [#permalink]

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04 Mar 2014, 10:29
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 !

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.
_________________

Kudos [?]: 135216 [0], given: 12673

Senior Manager
Joined: 06 Aug 2011
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Kudos [?]: 239 [0], given: 82

Re: M23 q 27 [#permalink]

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05 Mar 2014, 04:03
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 $$\pi{r^2}=100\pi$$.

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.
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Kudos [?]: 239 [0], given: 82

Math Expert
Joined: 02 Sep 2009
Posts: 42543

Kudos [?]: 135216 [0], given: 12673

Re: M23 q 27 [#permalink]

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05 Mar 2014, 05:28
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 $$\pi{r^2}=100\pi$$.

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.
_________________

Kudos [?]: 135216 [0], given: 12673

Senior Manager
Joined: 06 Aug 2011
Posts: 386

Kudos [?]: 239 [0], given: 82

Re: M23 q 27 [#permalink]

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05 Mar 2014, 07:34
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
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Kudos [?]: 239 [0], given: 82

Manager
Joined: 11 Sep 2013
Posts: 150

Kudos [?]: 151 [0], given: 187

Concentration: Finance, Finance
Re: M23 q 27 [#permalink]

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06 Jul 2014, 13:32
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.

Kudos [?]: 151 [0], given: 187

Math Expert
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Posts: 42543

Kudos [?]: 135216 [0], given: 12673

Re: M23 q 27 [#permalink]

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06 Jul 2014, 13:37
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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Re: M23 q 27   [#permalink] 06 Jul 2014, 13:37
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# M23 q 27

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