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# In the figure shown, if the side of the square is 40, what is the radi

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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14 Mar 2018, 00:11
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Difficulty:

95% (hard)

Question Stats:

26% (01:56) correct 74% (01:19) wrong based on 61 sessions

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In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

[Reveal] Spoiler:
Attachment:

Screenshot %2887%29.png [ 30.54 KiB | Viewed 689 times ]
[Reveal] Spoiler: OA

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Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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14 Mar 2018, 00:27
Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

[Reveal] Spoiler:
Attachment:
Screenshot %2887%29.png

DB is $$40\sqrt{2}$$
Diameter of bigger circle is 40
40\sqrt{2} = 2 * Diameter of small circle + 40(Diameter of bigger circle)
$$40\sqrt{2}$$ = 4 * radius of small circle + 40(Diameter of bigger circle)
Radius of small circle = $$(40\sqrt{2} - 40 ) / 4$$
A
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In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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Updated on: 26 Mar 2018, 23:54
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Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

[Reveal] Spoiler:
Attachment:
Screenshot %2887%29.png

IMO C
AS the diameter of large circle is 40 as the side of square is also 40
then diagonal of square is $$40\sqrt{2}$$
and this diagonal will include 2 small circles and 1 large circle so radius of small circle is approx
$$\frac{(40\sqrt{2} - 40)}{2}$$( 40root2-40/2)
so $$20(\sqrt{2}-1)$$ (this will be a bit bigger than diameter of smaller circle)
we need radius then divide it by 2 which make bit bigger than radius as $$10(\sqrt{2}-1)$$

but as you can see both small circles are not touching in the corner of the square then the answer will be little less than the above answer
above answer in terms of value is 10*0.3=3 correct answer will be little less
A.10*0.3= 3 our answer were bith less than 3
B.6 way greater than 3 incorrect
C.6/2.3= 2.3 (bit less correct)
D.40*0.3= 12 (very large)
E.40*0.3/2.3= 5.3(greater than 3 incorrect)

-------------------------------------------------------------------------------------------------------------------------------

If you like my explanation than please give me KUDOS

Originally posted by rishabhmishra on 14 Mar 2018, 00:33.
Last edited by rishabhmishra on 26 Mar 2018, 23:54, edited 1 time in total.
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Joined: 16 Sep 2016
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Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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14 Mar 2018, 01:30
Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

[Reveal] Spoiler:
Attachment:
The attachment Screenshot %2887%29.png is no longer available

IMO C.

This is a nice tricky question and I took over 4 mins to solve it. Everyone who have tried a solution have got a different answer and I am excited to find out the OA.

Please refer to the attached figure. We have to find t ( radius of the small circle ) as in the figure.

The figure is zoomed into the 1/4th part of the larger square.

The distance between one corner of the square and the circle is diagonal of the square of side 20 minus the radius of inscribed large circle of radius 20.
I have called the distance x. And x = $$20\sqrt{2} - 20$$

This is the trap option!

However this distance x is split between the radius of the circle t and and distance between the center of small circle and corner of large square t\sqrt{2}.

Hence by multiplying the x in the correct ratio we can find radius t.

t =$$x * 1/{\sqrt{2}+1}$$

t = $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Hence C.

Attachments

radius of circle.jpg [ 541.21 KiB | Viewed 541 times ]

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Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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25 Mar 2018, 05:23
1
KUDOS
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Attachments

IMG_20180325_175217.jpg [ 492.91 KiB | Viewed 328 times ]

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Joined: 14 Mar 2017
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Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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25 Mar 2018, 07:33
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????
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Joined: 14 Mar 2017
Posts: 3
Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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25 Mar 2018, 07:37
Dexter78424 wrote:
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????

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Joined: 16 Sep 2016
Posts: 207
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Re: In the figure shown, if the side of the square is 40, what is the radi [#permalink]

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25 Mar 2018, 07:37
Dexter78424 wrote:
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????

Hi Dexter78424,

Not quite clear what you are asking exactly. But the trick part of this question is - the ability to zoom in onto 1/4th of the larger square and focus on that.

You can see the detailed explanation in my post above & also in many other posts. The OA is correct -> Option (C)

Please go through those and ask specific doubts if you have any..

Best,
Re: In the figure shown, if the side of the square is 40, what is the radi   [#permalink] 25 Mar 2018, 07:37
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