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# In the figure above, a square with side of length √2 is inscribed in

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Joined: 02 Sep 2009
Posts: 50000
In the figure above, a square with side of length √2 is inscribed in  [#permalink]

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16 Nov 2017, 22:53
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Difficulty:

25% (medium)

Question Stats:

80% (00:58) correct 20% (01:06) wrong based on 62 sessions

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In the figure above, a square with side of length √2 is inscribed in a circle. If the area of the circle is kπ, what is the value of k?

(A) 1/2
(B) 3/4
(C) 1
(D) 2
(E) 2√2

Attachment:

2017-11-17_0947_001.png [ 3.36 KiB | Viewed 1000 times ]

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Re: In the figure above, a square with side of length √2 is inscribed in  [#permalink]

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17 Nov 2017, 00:27
The relationship between side of the square and radius of the circle is 2^1/2 to 1
So, kP=1^2*P
k=1
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In the figure above, a square with side of length √2 is inscribed in  [#permalink]

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17 Nov 2017, 15:44
Bunuel wrote:

In the figure above, a square with side of length √2 is inscribed in a circle. If the area of the circle is kπ, what is the value of k?

(A) 1/2
(B) 3/4
(C) 1
(D) 2
(E) 2√2

Attachment:
2017-11-17_0947_001.png

Use the square's diagonal to find diameter and radius of circle. Calculate circle's area. Set calculated area of circle equal to kπ.

The diagonal of a square with side s*: $$s\sqrt{2}$$
Given: $$s = \sqrt{2}$$
Diagonal length hence = $$\sqrt{2}*\sqrt{2}=2$$

Square's diagonal length =
length of circle's diameter, d
d = 2, and d = 2r
2 = 2r, r = 1

Area of circle = $$πr^2= (π)(1) = 1π$$
The area of the circle also = kπ
kπ = 1π
k = 1

**OR
$$side^2 + side^2 = diagonal^2$$
$$(\sqrt{2})^2 + (\sqrt{2})^2 = d^2$$
$$(2 + 2) = 4 = d^2$$
$$d = 2$$

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Re: In the figure above, a square with side of length √2 is inscribed in  [#permalink]

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18 Nov 2017, 01:50
Try finding out the length of the Diagonal of the square, then the radius of the circle. Finally you will get the value. k=1
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Re: In the figure above, a square with side of length √2 is inscribed in  [#permalink]

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20 Nov 2017, 12:29
Bunuel wrote:

In the figure above, a square with side of length √2 is inscribed in a circle. If the area of the circle is kπ, what is the value of k?

(A) 1/2
(B) 3/4
(C) 1
(D) 2
(E) 2√2

Attachment:
2017-11-17_0947_001.png

Since the diagonal of the inscribed square = the diameter of the circle, and since the diagonal of a square = side√2, we have √2(√2) = 2 = the diameter. So, the radius = 1, and the area of the circle is π. Now we can determine k:

kπ = π

k = 1

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Re: In the figure above, a square with side of length √2 is inscribed in &nbs [#permalink] 20 Nov 2017, 12:29
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