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If, in the figure above, arc BF is a semicircle having radius 12, and

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Kudos [?]: 135309 [0], given: 12686

If, in the figure above, arc BF is a semicircle having radius 12, and [#permalink]

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If, in the figure above, arc BF is a semicircle having radius 12, and C is a point, not shown, on arc BFs, which of the following gives all possible values of the perimeter P of pentagon ABCDE?

(A) 32 < P < 56
(B) 32 < P < 44
(C) 32 < P < 32 + 12√2
(D) P = 44
(E) P = 32

[Reveal] Spoiler:
Attachment:
2017-11-21_1004_002.png
2017-11-21_1004_002.png [ 5.54 KiB | Viewed 222 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135309 [0], given: 12686

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Kudos [?]: 38 [0], given: 89

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Re: If, in the figure above, arc BF is a semicircle having radius 12, and [#permalink]

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New post 20 Nov 2017, 23:29
Option A

Let’s says that the point C lies in the right side of the point D. In this case the maximum value of P is 12+24+4+12+4=56
Similarly if the point C lies on the left hand side of the point D the minimum value of P is 12+12+4+12+4=32
Hence 32<P<56


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Kudos [?]: 38 [0], given: 89

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Kudos [?]: 17 [0], given: 290

Re: If, in the figure above, arc BF is a semicircle having radius 12, and [#permalink]

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New post 20 Nov 2017, 23:36
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Bunuel wrote:
Image
If, in the figure above, arc BF is a semicircle having radius 12, and C is a point, not shown, on arc BFs, which of the following gives all possible values of the perimeter P of pentagon ABCDE?

(A) 32 < P < 56
(B) 32 < P < 44
(C) 32 < P < 32 + 12√2
(D) P = 44
(E) P = 32

[Reveal] Spoiler:
Attachment:
2017-11-21_1004_002.png


For the minimum Range Point C should lie Close to B and for Maximum Range Point C should lie close to F.

32 < P < 56

Kudos [?]: 17 [0], given: 290

Re: If, in the figure above, arc BF is a semicircle having radius 12, and   [#permalink] 20 Nov 2017, 23:36
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If, in the figure above, arc BF is a semicircle having radius 12, and

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