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In the figure above, the circles with centers A and B are tangent to

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In the figure above, the circles with centers A and B are tangent to [#permalink]

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New post 29 Nov 2017, 22:03
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In the figure above, the circles with centers A and B are tangent to each other at C, and are tangents to the lines m and n at F and D. If the radius of each of the circles is √2 and m is parallel to n, what is the length of EF?

(A) 2√2 + 1
(B) 2√2 + 2
(C) 2√2 + 3
(D) 3√2
(E) 3√2 + 1


[Reveal] Spoiler:
Attachment:
2017-11-30_1000.png
2017-11-30_1000.png [ 10.13 KiB | Viewed 266 times ]
[Reveal] Spoiler: OA

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In the figure above, the circles with centers A and B are tangent to [#permalink]

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New post 29 Nov 2017, 22:46
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Bunuel I have a doubt. Without knowing the angle between the line AB and EF how to calculate the distance between ED? Please help.

Please refer the attached figure. For each case the length will be different.

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In the figure above, the circles with centers A and B are tangent to [#permalink]

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New post 30 Nov 2017, 01:37
Hi, I tried an overly simplistic approach, and got the answer E.
It took me 10 seconds after trying all the theories I knew. Basically EF consists of 3 radi's plus something in the middle , so it must be 3√2 + 1. ( assuming the line opposite the radius is parallel to the radius.

Many assumptions taken, still not a concrete answer.

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In the figure above, the circles with centers A and B are tangent to   [#permalink] 30 Nov 2017, 01:37
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In the figure above, the circles with centers A and B are tangent to

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