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# In the figure above, each arc is a semicircle. If AB = BD, and BC = CD

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Joined: 02 Sep 2009
Posts: 50078
In the figure above, each arc is a semicircle. If AB = BD, and BC = CD  [#permalink]

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28 Nov 2017, 21:09
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Difficulty:

25% (medium)

Question Stats:

94% (01:53) correct 6% (01:39) wrong based on 24 sessions

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In the figure above, each arc is a semicircle. If AB = BD, and BC = CD, what is the ratio length of arc AD / length of arc CD?

(A) 4π/3
(B) 3π/2
(C) 3/1
(D) 4/1
(E) 9/2

Attachment:

2017-11-29_0805.png [ 4.1 KiB | Viewed 492 times ]

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In the figure above, each arc is a semicircle. If AB = BD, and BC = CD  [#permalink]

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28 Nov 2017, 21:25
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Re: In the figure above, each arc is a semicircle. If AB = BD, and BC = CD  [#permalink]

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01 Dec 2017, 07:55
Bunuel wrote:

In the figure above, each arc is a semicircle. If AB = BD, and BC = CD, what is the ratio length of arc AD / length of arc CD?

(A) 4π/3
(B) 3π/2
(C) 3/1
(D) 4/1
(E) 9/2

Attachment:
2017-11-29_0805.png

We can let BC = CD = 1; thus AB = BD = 2. Therefore:

arc AD = 1/2 x (2 x π x 2) = 2π

and

arc CD = 1/2 x (2 x π x 1/2) = π/2

Thus, arc AD / arc CD = 2π/(π/2) = 2/(1/2) = 4/1.

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Re: In the figure above, each arc is a semicircle. If AB = BD, and BC = CD &nbs [#permalink] 01 Dec 2017, 07:55
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