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# If a square is inscribed in a circle of radius r as shown above, then

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Math Expert
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If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

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21 Nov 2017, 23:19
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Difficulty:

25% (medium)

Question Stats:

84% (01:20) correct 16% (01:25) wrong based on 52 sessions

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If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:

2017-11-21_1033.png [ 4.39 KiB | Viewed 4502 times ]

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Re: If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

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21 Nov 2017, 23:32
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Diagonal of Square = 2r = $$x\sqrt{2}$$
Area of square = $$(\sqrt{2}r)^2$$
=2r^2

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If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

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26 Nov 2017, 22:43
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Derive side length of square from its diagonal.

Diagonal, d, of square = $$2r$$

Side, s, of square*:

$$s\sqrt{2} = d$$

$$s = \frac{d}{\sqrt{2}}$$

$$s=\frac{2r}{\sqrt{2}}$$ *$$\frac{\sqrt{2}}{\sqrt{2}}$$

$$s= \frac{2r\sqrt{2}}{2}=r\sqrt{2}$$

Area of square = $$s^2$$

A= $$(r\sqrt{2})^2 = 2r^2$$

* derived from
$$s^2 + s^2 = d^2$$
$$2s^2 = d^2$$
$$\sqrt{2}*\sqrt{s^2} = \sqrt{d^2}$$
$$s\sqrt{2} = d$$
$$s = \frac{d}{\sqrt{2}}$$

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Re: If a square is inscribed in a circle of radius r as shown above, then  [#permalink]

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29 Nov 2017, 10:57
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

Attachment:
2017-11-21_1033.png

Since the radius is r, the circle’s diameter = diagonal of square = 2r.

Since diagonal = side√2:

2r = side√2

2r/√2 = side

Thus, area of the square = (2r/√2)^2 = 4r^2/2= 2r^2.

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Re: If a square is inscribed in a circle of radius r as shown above, then &nbs [#permalink] 29 Nov 2017, 10:57
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