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In the figure above, the circle is inscribed in a square tha

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In the figure above, the circle is inscribed in a square tha [#permalink] New post   06 Oct 2018, 15:12
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In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

(A) \(\frac{25\pi}{4}\)
(B) \(\frac{25\pi}{2}\)
(C) \(25\pi\)
(D) \(50\pi\)
(E) \(\frac{625\pi}{16}\)
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B
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Re: In the figure above, the circle is inscribed in a square tha [#permalink] New post   15 Oct 2018, 04:29
area of the circle = 50
area of the circle = \(side^2\)
\(s^2\) = 50
s =\(5\sqrt{2}\)
This is also the diameter of the circle
therefore, radius = \(5/\sqrt{2}\)
area of the circle = \(25\pi/2\)
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In the figure above, the circle is inscribed in a square tha [#permalink] New post   04 Jan 2024, 22:45
The area of the square is \(50\).

The length of its side is\( \sqrt{50}\) = diameter of the inscribed circle.

The radius of the inscribed circle = \(\frac{\sqrt{50}}{2}\)

\(\text{Area of the circle} = \pi \times r^2 = \pi \times (\frac{\sqrt{50}}{2})^2 = \pi \frac{50}{4} = \frac{25 \pi}{2}\)

The answer is Choice B
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In the figure above, the circle is inscribed in a square tha [#permalink]
04 Jan 2024, 22:45
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