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# The figure above shows a cord around two circular disks. If

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The figure above shows a cord around two circular disks. If [#permalink]

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19 Oct 2006, 10:35
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The figure above shows a cord around two circular disks. If the radii of the two disks are 80 centimeters and 60 centimeters, respectively, what is the total length, in centimeters, of the cord?

(A) 210π
(B) 210π+ 280
(C) 280π
(D) 280π + 80
(E) 280π+ 280
[Reveal] Spoiler: OA

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19 Oct 2006, 10:59
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Since the tangents form squares with the radii.

the total length as tangents = 2*80+2*60 = 280

and the total lenght wound around the circles = 270deg/360deg * 2*pi*80
=120pi

for the second circle similarly 90pi
therfore 210pi+280
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19 Oct 2006, 11:41
Oh yes, this one was obvious....

Misinterpreted the question a bit....
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10 Sep 2011, 07:02
important thing where i got stuck...
i found this on another site..its really help full.

I feel we are not supposed to take the literal meaning of the term "cord" {lineseg that lies inside the cirlce with its ends lieing on the circle"} as its meaning but as a piece of wire/some material that goes around the 2 circles.

so.........

Since the tangents form squares with the radii.

the total length as tangents = 2*80+2*60 = 280

and the total lenght wound around the circles = 270deg/360deg * 2*pi*80
=120pi

for the second circle similarly 90pi
therfore 210pi+280
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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02 May 2014, 04:25
bunuel, could you please explain this.

thanks.
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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07 Oct 2014, 06:26
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Lets me try to explain, this one is more of a verbal question then a quant question. If you read the question correctly, its say "The figure above shows a cord around two circular disks." This makes the question tough but concept it test is easy.

2 squares total chord length: 280
2 arcs for the circle: 210π

So total: 210π+280

bunuel, could you please explain this.

thanks.

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The figure above shows a cord around two circular disks. If [#permalink]

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08 Oct 2014, 01:09
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SimaQ wrote:
Attachment:
Circles.png
The figure above shows a cord around two circular disks. If the radii of the two disks are 80 centimeters and 60 centimeters, respectively, what is the total length, in centimeters, of the cord?

(A) 210π
(B) 210π+ 280
(C) 280π
(D) 280π + 80
(E) 280π+ 280

A chord (or a thread) is wrapped around the two disks as shown. The length of the thread is

Part of circumference of bigger disk + the two intersecting straight lines + Part of circumference of smaller disk

Length of the two straight lines: We see from the figure that there are 2 squares. The length of the straight lines will be 80 + 60 + 80 + 60 = 280

Part of circumference of bigger disk: The arc that forms the 90 degree angle is not included so the rest of it makes 270 degree angle. Circumference = $$(270/360) * 2*\pi*80 = 120*\pi$$

Part of circumference of smaller disk: The arc that forms the 90 degree angle is not included so the rest of it makes 270 degree angle. Circumference = $$(270/360) * 2*\pi*60 = 90*\pi$$

Total length of chord = $$280 + 120*\pi + 90*\pi = 280 + 210*\pi$$
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The figure above shows a cord around two circular disks. If [#permalink]

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08 Oct 2014, 04:12

In any case, this is the way I did it:
(270/360)*2*pie*80 + (270/360)*2*pie*60. that gave me 210 pie and I simply chose option B. But let's try and work out the remaining portion:
If I draw a line dividing the left square into two equal halves, I get an isosceles triangle. That means the two pieces of chord extending from the circle on the left are 80 cm each, and the two extending from the circle on the right are 60 cms each.

Ans is 210pie +80+80+60+60= B
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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21 Oct 2014, 20:30
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$$Length = \frac{3}{4} * 160\pi + \frac{3}{4} * 120\pi + 2*80 + 2*60$$

$$= 120\pi + 90\pi + 280$$

$$= 210\pi + 280$$

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Re: The figure above shows a cord around two circular disks. If [#permalink]

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13 Jul 2015, 06:41
PareshGmat wrote:
$$Length = \frac{3}{4} * 160\pi + \frac{3}{4} * 120\pi + 2*80 + 2*60$$

$$= 120\pi + 90\pi + 280$$

$$= 210\pi + 280$$

Exactly how I approached it!
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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17 Mar 2016, 03:53
how you deduce that both rectangles are squares...
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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17 Mar 2016, 04:08
vipulgoel wrote:
how you deduce that both rectangles are squares...

We have three 90 degree angles, thus the fourth one also must be 90 degree angle. So, we have a rectangle. Next, the two adjacent sides are equal to the radii, so they are equal. A rectangle which has equal width and length is a square.

Hope it's clear.
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Re: The figure above shows a cord around two circular disks. If [#permalink]

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19 Aug 2016, 09:59
SimaQ wrote:
Attachment:
Circles.png
The figure above shows a cord around two circular disks. If the radii of the two disks are 80 centimeters and 60 centimeters, respectively, what is the total length, in centimeters, of the cord?

(A) 210π
(B) 210π+ 280
(C) 280π
(D) 280π + 80
(E) 280π+ 280

The cord passed through 3/4 of the circumference of both the circles and the 2 tangents.

So total length = $$3/4 *(2 *\pi * 80 + 2 * \pi * 60) + 2 ( 80+60)$$ =$$210\pi + 280$$

Re: The figure above shows a cord around two circular disks. If   [#permalink] 19 Aug 2016, 09:59
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