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# In the figure above, what is the area of the square inscribed in the

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Math Expert
Joined: 02 Sep 2009
Posts: 52294
In the figure above, what is the area of the square inscribed in the  [#permalink]

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23 Nov 2017, 22:17
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:05) correct 32% (01:18) wrong based on 36 sessions

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In the figure above, what is the area of the square inscribed in the circle of radius a?

(A) 2a
(B) √2*a^2
(C) a^2
(D) 2a^2
(E) 4a^2

Attachment:

2017-11-23_2025.png [ 5.3 KiB | Viewed 605 times ]

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In the figure above, what is the area of the square inscribed in the  [#permalink]

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24 Nov 2017, 05:32

The diameter of the circle is the diagonal of the square
Since the radius of the circle is a, the diameter will be 2a
Side√2 = 2a

The side of the square is $$\frac{(√2*√2a)}{√2} = √2*a$$

Therefore, the area of the square with side($$√2*a$$) is $$2a^2$$(Option D)
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Re: In the figure above, what is the area of the square inscribed in the  [#permalink]

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24 Nov 2017, 07:45
1
In the figure above, what is the area of the square inscribed in the circle of radius a?

(A) 2a
(B) √2*a^2
(C) a^2
(D) 2a^2
(E) 4a^2

1) Let x be a side of the square
2) diametr AC is equal to 2a
3) In the right triangle ABC:
$$x^2 + x^2 = (2a)^2$$
$$2x^2 = 4a^2$$
$$x^2 = 2a^2$$

x^2 is equal to area of the square ABCD so that is 2a^2 ; the answer is D
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a square in the circle.jpg [ 31.08 KiB | Viewed 458 times ]

Re: In the figure above, what is the area of the square inscribed in the &nbs [#permalink] 24 Nov 2017, 07:45
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