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

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

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New post 21 Nov 2017, 23:19
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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
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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New post 21 Nov 2017, 23:32
Bunuel wrote:
Image
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

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

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New post 26 Nov 2017, 22:43
Bunuel wrote:
Image
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= \((r\sqrt{2})^2 = 2r^2\)

Answer E

* 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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New post 29 Nov 2017, 10:57
Bunuel wrote:
Image
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.

Answer: E
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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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