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# In the figure above, the smaller circle is inscribed in the square

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Joined: 02 Sep 2009
Posts: 52296
In the figure above, the smaller circle is inscribed in the square  [#permalink]

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10 Jan 2019, 01:15
00:00

Difficulty:

35% (medium)

Question Stats:

81% (01:24) correct 19% (00:16) wrong based on 16 sessions

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In the figure above, the smaller circle is inscribed in the square and the square is inscribed in the larger circle. If the length of each side of the square is s, what is the ratio of the area of the larger circle to the area of the smaller circle?

A. $$2\sqrt{2}:1$$

B. $$2:1$$

C. $$\sqrt{2}:1$$

D. $$2s:1$$

E. $$s\sqrt{2}:1$$

Attachment:

2019-01-10_1311.png [ 22.06 KiB | Viewed 163 times ]

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Re: In the figure above, the smaller circle is inscribed in the square  [#permalink]

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10 Jan 2019, 01:50
In the figure above, the smaller circle is inscribed in the square and the square is inscribed in the larger circle. If the length of each side of the square is s, what is the ratio of the area of the larger circle to the area of the smaller circle?

Area of an circle inscribed in a square = $$(Pi/4)*Area of the square$$
= $$(Pi/4)*S^2$$

Area of a circle circumscribed in a square = (Pi/2)*Area of the square
= $$(Pi/2)*S^2$$

ratio of the area of the larger circle to the area of the smaller circle = $$((Pi/2)*S^2)/((Pi/4)*S^2)$$ = 2:1

Option B is correct
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Re: In the figure above, the smaller circle is inscribed in the square  [#permalink]

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10 Jan 2019, 04:22
Bunuel wrote:

In the figure above, the smaller circle is inscribed in the square and the square is inscribed in the larger circle. If the length of each side of the square is s, what is the ratio of the area of the larger circle to the area of the smaller circle?

A. $$2\sqrt{2}:1$$

B. $$2:1$$

C. $$\sqrt{2}:1$$

D. $$2s:1$$

E. $$s\sqrt{2}:1$$

Attachment:
2019-01-10_1311.png

diameter of smaller circle ; s and radius s/2

diameter of larger circule : s sqrt2 ; radius s/sqrt2

so area : pi * s^2 /2 * 4/s^2
solving we get 2:1 IMO B
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Re: In the figure above, the smaller circle is inscribed in the square &nbs [#permalink] 10 Jan 2019, 04:22
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