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

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Math Expert
Joined: 02 Sep 2009
Posts: 42605

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

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16 Nov 2017, 21:53
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Question Stats:

80% (00:33) correct 20% (00:49) wrong based on 41 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

[Reveal] Spoiler:
Attachment:

2017-11-17_0947_001.png [ 3.36 KiB | Viewed 493 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135629 [0], given: 12705

Senior Manager
Joined: 05 Dec 2016
Posts: 253

Kudos [?]: 27 [0], given: 49

Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: In the figure above, a square with side of length √2 is inscribed in [#permalink]

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16 Nov 2017, 23:27
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

Kudos [?]: 27 [0], given: 49

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

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

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17 Nov 2017, 14:44
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

[Reveal] Spoiler:
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
$$side^2 + side^2 = diagonal^2$$
$$(\sqrt{2})^2 + (\sqrt{2})^2 = d^2$$
$$(2 + 2) = 4 = d^2$$
$$d = 2$$

Kudos [?]: 402 [0], given: 645

Intern
Joined: 05 Nov 2012
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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, 00:50
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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Target Test Prep Representative
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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, 11:29
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

[Reveal] Spoiler:
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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Kudos [?]: 1018 [0], given: 3

Re: In the figure above, a square with side of length √2 is inscribed in   [#permalink] 20 Nov 2017, 11:29
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