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A circle is circumscribed around a square such that all the angles of

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fitzpratik
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A circle is circumscribed around a square such that all the angles of [#permalink] New post   25 Aug 2017, 20:22
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A circle is circumscribed around a square such that all the angles of the squares lie on circumference. What is the area of the circle, if area of the square is 100 units?

A. 131

B. 137

C. 157

D. 161

E. 174
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VyshakhR1995
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Re: A circle is circumscribed around a square such that all the angles of [#permalink] New post   26 Aug 2017, 02:03
The side of the square will be 10...
The diameter of the circle will be 10\sqrt{2}
The radius will be 5\sqrt{2}

Area equals 3.14*25*2
= 157
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Re: A circle is circumscribed around a square such that all the angles of [#permalink] New post   26 Aug 2017, 23:02
VyshakhR1995 wrote:
The side of the square will be 10...
The diameter of the circle will be 10\sqrt{2}
The radius will be 5\sqrt{2}

Area equals 3.14*25*2
= 157


this will hold true for all circumscribed squares.

So we can get a general formula
Area of a circle = 1.57 X Area of square it circumscribes
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Re: A circle is circumscribed around a square such that all the angles of [#permalink] New post   20 Sep 2017, 04:44
fitzpratik wrote:
VyshakhR1995 wrote:
The side of the square will be 10...
The diameter of the circle will be 10\sqrt{2}
The radius will be 5\sqrt{2}

Area equals 3.14*25*2
= 157


this will hold true for all circumscribed squares.

So we can get a general formula
Area of a circle = 1.57 X Area of square it circumscribes

is there any formula for Area of circle if we know the are of square it inscribes?
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Re: A circle is circumscribed around a square such that all the angles of [#permalink] New post   20 Sep 2017, 05:07
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johneagle2776 wrote:
fitzpratik wrote:
VyshakhR1995 wrote:
The side of the square will be 10...
The diameter of the circle will be 10\sqrt{2}
The radius will be 5\sqrt{2}

Area equals 3.14*25*2
= 157


this will hold true for all circumscribed squares.

So we can get a general formula
Area of a circle = 1.57 X Area of square it circumscribes

is there any formula for Area of circle if we know the are of square it inscribes?


Say the area of an inscribed square is x unit^2 --> the area of a circle = \(\frac{diagonal^2}{2} = x\)

The diagonal of an inscribed square = the diameter of a circle.

The area of a circle = \(\pi r^2 = \pi *(\frac{diameter}{2})^2 = \pi *(\frac{diagonal}{2})^2 = \pi * \frac{diagonal^2}{4}=\pi *\frac{x}{2}\).

But memorising this formula would be waste of time. It's MUCH better to know/understand the logic behind it.
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Re: A circle is circumscribed around a square such that all the angles of [#permalink] New post   25 Sep 2017, 18:06
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fitzpratik wrote:
A circle is circumscribed around a square such that all the angles of the squares lie on circumference. What is the area of the circle, if area of the square is 100 units?

A. 131

B. 137

C. 157

D. 161

E. 174


Since the area of the square is 100 units, each side is 10.

Since the diagonal of the square = the diameter of the circle, the diameter is 10√2, and thus the radius is 5√2.

Finally, the area of the circle is π(5√2)^2 = 50π ≈ 50 x 3.14 = 157.

Answer: C
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Re: A circle is circumscribed around a square such that all the angles of [#permalink]
25 Sep 2017, 18:06
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