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# The figure above shows the shape of a tunnel entrance. If

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Manager
Joined: 30 Mar 2007
Posts: 179
The figure above shows the shape of a tunnel entrance. If [#permalink]

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18 May 2007, 23:42
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The figure above shows the shape of a tunnel entrance. If the curved portion is of a circle and the base of the entrance is 12 feet across, what is the perimeter, in feet, of the curved portion of the entrance'?

(A) 9pi
(B) 12pi
(C) 9pi rt(2)
(D) 18pi
(E) 9pi/rt(2)

so how do you solve this??
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Manager
Joined: 11 Mar 2007
Posts: 84

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19 May 2007, 00:53
Himalayan, can you please explain, how did u get the answer.... i am lost..
VP
Joined: 08 Jun 2005
Posts: 1145

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19 May 2007, 06:47
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the "trick" is to know that you can draw an inscribed square inside the tunnel. the base of the square will then be the floor of the tunnel.

when you draw an inscribed square, you can divide it into two 45:45:90 degrees triangles.

knowing that the sides of the triangle are at a ratio of 1:1:sqrt(2) to the hypotenuse and knowing (from the stem) that one of the side is 12 will help you find the hypotenuse (equal to the circle diameter).

1:1:sqrt(2) --- (ratio)

12:12:12*sqrt(2)

hence 12*sqrt(2) is the diameter and 6*sqrt(2) is the radius.

Knowing the diameter we can find the perimeter of the whole circle

2*pi*r = 2*pi*(6*sqrt(2)) = 12*pi*sqrt(2) the perimeter of the whole circle !

we still have to find only the perimeter of the "semi" circle.

one of the square sides is the base. that means that the perimeter is only 3/4 of the whole circale (I can prove this but just belive me fo now).

and the perimeter of 3/4 circle is 3/4*12*pi*sqrt(2) = 9*pi*sqrt(2)

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Joined: 08 Oct 2006
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19 May 2007, 07:09
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KillerSquirrel wrote:
the "trick" is to know that you can draw an inscribed square inside the tunnel. the base of the square will then be the floor of the tunnel.

Is this defacto standard?
It can be a square or a rectangle and the other 2 vertices's may not necessarily touch the circumference of the circle.
Am I missing something? arent we supposed to 'not' assume extra /outside information
VP
Joined: 08 Jun 2005
Posts: 1145

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19 May 2007, 08:21
manish.gmat wrote:
KillerSquirrel wrote:
the "trick" is to know that you can draw an inscribed square inside the tunnel. the base of the square will then be the floor of the tunnel.

Is this defacto standard?
It can be a square or a rectangle and the other 2 vertices's may not necessarily touch the circumference of the circle.
Am I missing something? arent we supposed to 'not' assume extra /outside information

yes ! it's a rule - a rectangular shape inscribed (meaning - touching all sides) inside a circle will always be a square !

Director
Joined: 26 Feb 2006
Posts: 899

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19 May 2007, 12:46
KillerSquirrel wrote:
manish.gmat wrote:
KillerSquirrel wrote:
the "trick" is to know that you can draw an inscribed square inside the tunnel. the base of the square will then be the floor of the tunnel.

Is this defacto standard?
It can be a square or a rectangle and the other 2 vertices's may not necessarily touch the circumference of the circle.
Am I missing something? arent we supposed to 'not' assume extra /outside information

yes ! it's a rule - a rectangular shape inscribed (meaning - touching all sides) inside a circle will always be a square !

though I assumed the same concept but it is not always true cuz a ractangle can also be inscribed into a circle. right???????
VP
Joined: 08 Jun 2005
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19 May 2007, 13:01
Himalayan wrote:
KillerSquirrel wrote:
manish.gmat wrote:
KillerSquirrel wrote:
the "trick" is to know that you can draw an inscribed square inside the tunnel. the base of the square will then be the floor of the tunnel.

Is this defacto standard?
It can be a square or a rectangle and the other 2 vertices's may not necessarily touch the circumference of the circle.
Am I missing something? arent we supposed to 'not' assume extra /outside information

yes ! it's a rule - a rectangular shape inscribed (meaning - touching all sides) inside a circle will always be a square !

though I assumed the same concept but it is not always true cuz a ractangle can also be inscribed into a circle. right???????

Himalayan

if an a rectangular (and not a square) is inscribed into a circle its not a circle but an ellipse. (see also OG 11 - page 133).
Intern
Status: I know my GPA is brilliant.
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Re: The figure above shows the shape of a tunnel entrance. If [#permalink]

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17 Sep 2012, 09:50
1. Draw a diameter parallel to base of the entrance and mark the center as "O".

2. Let's name one corner of the base as "A" and other as "B".

3. Draw two connectors, one from "A" to "O" and the other from "B" to "O".

4. Complete the figure of circle. Arc AB is equal to 90 degrees since it is equal to 1/4 of total circle.

5. Turn back to constructed triangle. Angle AOB is equal to 90 because arc AB is also equal to 90.

6. Moreover triangle AOB is isosceles because both AO and OB are equal to radius of the circle.

7. In that case, both AO and OB must be equal to 12^(1/2). Answer is "C".
Director
Joined: 22 Mar 2011
Posts: 612
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Re: The figure above shows the shape of a tunnel entrance. If [#permalink]

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17 Sep 2012, 11:43
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Jamesk486 wrote:
The figure above shows the shape of a tunnel entrance. If the curved portion is of a circle and the base of the entrance is 12 feet across, what is the perimeter, in feet, of the curved portion of the entrance'?

(A) 9pi
(B) 12pi
(C) 9pi rt(2)
(D) 18pi
(E) 9pi/rt(2)

so how do you solve this??

The correct question is:

The figure above (in the attachment) shows the shape of a tunnel entrance. If the curved portion is 3/4 of a circle and the base of the entrance is 12 feet across, what is the perimeter, in feet, of the curved portion of the entrance'?

Without the information in red the question cannot be solved. Given that piece of information, it follows that the base is one of the sides of an inscribed square in the circle.
For any circle, there are infinitely many rectangles which can be inscribed in it. In particular, squares are also inscribable in a circle.
All the comments stating that a rectangle inscribed in a circle must be a square are completely wrong!
Also, in an ellipse, infinitely many rectangles and a uniques square having sides parallel to the axes of the ellipse can be inscribed.

Please, check the accuracy of the question before posting.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 21 Aug 2012
Posts: 199
Concentration: General Management, Operations
Schools: HBS '19 (S)
GMAT 1: 740 Q49 V42
Re: The figure above shows the shape of a tunnel entrance. If [#permalink]

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02 Jan 2013, 06:07
damn tricky ... do we get such questions in GMAT??
Manager
Joined: 07 May 2013
Posts: 109
Re: The figure above shows the shape of a tunnel entrance. If [#permalink]

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08 Nov 2013, 21:35
I don't think it's a GMAT question......too many assumptions required to solve it.
Manager
Joined: 07 May 2013
Posts: 109
Re: The figure above shows the shape of a tunnel entrance. If [#permalink]

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08 Nov 2013, 21:35
I don't think it's a GMAT question......too many assumptions required to solve it.
Re: The figure above shows the shape of a tunnel entrance. If   [#permalink] 08 Nov 2013, 21:35
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