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# The figure above shows portions of two circles with centers at A and C

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Math Expert
Joined: 02 Sep 2009
Posts: 47015
The figure above shows portions of two circles with centers at A and C [#permalink]

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23 Nov 2017, 01:21
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78% (01:24) correct 22% (01:59) wrong based on 18 sessions

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The figure above shows portions of two circles with centers at A and C respectively, and square ABCD with side of length s. What is the perimeter of the curved figure in terms of s?

(A) 4πs/3
(B) 3πs/2
(C) 2πs
(D) 3πs
(E) 4πs

Attachment:

2017-11-23_1215.png [ 7.13 KiB | Viewed 449 times ]

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Joined: 26 Sep 2017
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The figure above shows portions of two circles with centers at A and C [#permalink]

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23 Nov 2017, 02:02

Required Perimeter = Major Arc BD (circle with center A) + Major Arc BD (circle with center C)

P= 2*$$\pi$$*s*270/360 + 2*$$\pi$$*s*270/360

P= 3$$\pi$$s
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Joined: 22 May 2016
Posts: 1825
The figure above shows portions of two circles with centers at A and C [#permalink]

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23 Nov 2017, 09:42
Bunuel wrote:

The figure above shows portions of two circles with centers at A and C respectively, and square ABCD with side of length s. What is the perimeter of the curved figure in terms of s?

(A) 4πs/3
(B) 3πs/2
(C) 2πs
(D) 3πs
(E) 4πs

Attachment:
2017-11-23_1215.png

Perimeter = $$\frac{3}{4}$$ circumference of one circle * 2

Vertex A of square ABCD = 90°. That 90° "cuts" (shortens) the perimeter of circle with center A by $$\frac{90}{360}=\frac{1}{4}$$

One part of the perimeter of the curved figure hence is $$\frac{3}{4}$$ of the circumference of Circle A.

Vertex C of the square does exactly the same thing to the circle with center C.

So perimeter of curved figure =
$$\frac{3}{4}$$ circumference of Circle A +
$$\frac{3}{4}$$ circumference of Circle C

Radius of both circles = square's side length = $$s$$

Circumference of each circle:$$2πr = 2πs$$

Perimeter of curved figure:
$$(2) * (\frac{3}{4} *2πs)=\frac{12πs}{4}=3πs$$

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The figure above shows portions of two circles with centers at A and C   [#permalink] 23 Nov 2017, 09:42
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