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# The figure above represents a circular window with centre C. How long

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The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 02:52
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Difficulty:

55% (hard)

Question Stats:

57% (01:35) correct 43% (01:58) wrong based on 42 sessions

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The figure above represents a circular window with centre C. How long would a horizontal curtain rod have to be to span the window 8 inches directly above point c?

(1) A curtain rod that crosses the window 12 inches above C is 32 inches long
(2) The window has a radius of 20 inches

Attachment:

2019-05-26_1350.png [ 9.53 KiB | Viewed 564 times ]

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Re: The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 03:04
2
When the curtain rod is 8 inches above the centre, and lines are drawn from centre to ends of the rod, we will have 2 congruent right angled triangles, each with height 8 inches whose hypotenuse is equal to the radius of the circle and base, half the length of the curtain rod.

So if we know the radius, we can use pythagoras to calculate the length of the rod.

So essentially, we just need to know if we can calculate the radius of the circle.

Statement (1) gives us the length of the rod when height is 12 inches from centre. Using this length and height, we can calculate the radius of the circle.

(1) is sufficient

Statement (2) directly gives us the radius of the circle

(2) is sufficient

Hit Kudos if this helped!
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Re: The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 03:22
Statement 1:

given the length of a chord is 32 inches when perpendicular distance from the centre is 12 inches.

Length of a chord=2*sqrt(r^2-d^2) ; r=radius & d=perpendicular distance from the centre.
32=2*sqrt(r^2-10^2) from this we can get the value of r and thereby calculate the distance of the chord whose perpendicular distance from the centre is 8 inches: Statement 1 is sufficient.

Statement 2:

As stated earlier we have r=20 and d=8 so length of the chord can be determined and statement 2 is sufficient.

IMO Option D
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Re: The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 06:39
1
Bunuel wrote:

The figure above represents a circular window with centre C. How long would a horizontal curtain rod have to be to span the window 8 inches directly above point c?

(1) A curtain rod that crosses the window 12 inches above C is 32 inches long
(2) The window has a radius of 20 inches

Attachment:
The attachment 2019-05-26_1350.png is no longer available

If we can find r- radius of the circle we can easily find the length of the chord. Check the diagram:-

Attachment:

IMG_20190526_190502__01.jpg [ 1.68 MiB | Viewed 369 times ]

Now, using Pythagoras we can find r from statement/diagram 1.
And r is given in statement/diagram 2.

So, E: Each statement independently sufficient.
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Re: The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 14:52
firas92 wrote:
When the curtain rod is 8 inches above the centre, and lines are drawn from centre to ends of the rod, we will have 2 congruent right angled triangles, each with height 8 inches whose hypotenuse is equal to the radius of the circle and base, half the length of the curtain rod.

So if we know the radius, we can use pythagoras to calculate the length of the rod.

So essentially, we just need to know if we can calculate the radius of the circle.

Statement (1) gives us the length of the rod when height is 12 inches from centre. Using this length and height, we can calculate the radius of the circle.

(1) is sufficient

Statement (2) directly gives us the radius of the circle

(2) is sufficient

.

Hit Kudos if this helped!

Hey ,

Could you please draw and show the figures .

I am unable to visualize and comprehend this problem.

It would be very helpful .
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Re: The figure above represents a circular window with centre C. How long  [#permalink]

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26 May 2019, 16:55
a1997g wrote:
firas92 wrote:
When the curtain rod is 8 inches above the centre, and lines are drawn from centre to ends of the rod, we will have 2 congruent right angled triangles, each with height 8 inches whose hypotenuse is equal to the radius of the circle and base, half the length of the curtain rod.

So if we know the radius, we can use pythagoras to calculate the length of the rod.

So essentially, we just need to know if we can calculate the radius of the circle.

Statement (1) gives us the length of the rod when height is 12 inches from centre. Using this length and height, we can calculate the radius of the circle.

(1) is sufficient

Statement (2) directly gives us the radius of the circle

(2) is sufficient

.

Hit Kudos if this helped!

Hey ,

Could you please draw and show the figures .

I am unable to visualize and comprehend this problem.

It would be very helpful .

a1997g check my post, I've uploaded my solution with diagram.
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I never gave up what I wanted-
Re: The figure above represents a circular window with centre C. How long   [#permalink] 26 May 2019, 16:55
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