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# A 3 by 4 rectangle is inscribed in a circle. What is the area of the

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A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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20 Nov 2017, 22:20
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Difficulty:

25% (medium)

Question Stats:

89% (00:47) correct 11% (01:10) wrong based on 34 sessions

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A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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20 Nov 2017, 22:26
\sqrt{}
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

l = 3, b = 5
2r = 5... A= 6.25pi
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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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21 Nov 2017, 00:06
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

The diagonal of the rectangle is 5 since we have pythagoras right triangle 3-4-5 .
This diagonal is the diameter of the circle .
Area = pi* (5/2)^2 = 6.25 pi

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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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21 Nov 2017, 00:15
A rectangle being inscribed in a circle means that the diagonal of the rectangle will become the diameter of the circle.

Diagonal of a rectangle = $$\sqrt{L^2 + B^2}$$ => $$\sqrt{4^2 + 3^2}$$ => $$\sqrt{16+9}$$ => $$\sqrt{25}$$ = 5
As in this case, diagonal = diameter, hence, radius of the circle becomes 2.5

Area of a circle = $$\pi$$$$r^2$$ => $$\pi$$*$$2.5^2$$ => 6.25$$\pi$$
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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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21 Nov 2017, 07:31
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

Diagonal of the rectangle = Diameter of the Circle.

Diameter of the rectangle is 5 ( As Its a right angled triangle with sides 3,4,5)

So, Radius is $$2.5$$

Thus, area will be $$2.5^2π$$ = $$6.25π$$ , answer will be (A)
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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the  [#permalink]

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27 Nov 2017, 10:50
Bunuel wrote:
A 3 by 4 rectangle is inscribed in a circle. What is the area of the circle?

(A) 6.25π
(B) 9π
(C) 12.25π
(D) 16π
(E) 25π

When a rectangle is inscribed in a circle, its diagonal is equal to the diameter of the circle. Furthermore, the diagonal of the rectangle divides the rectangle into two congruent right triangles with the diagonal being the hypotenuse. Since the two legs of the right triangle are 3 and 4,respectively, the hypotenuse must be 5, and thus, the diameter of the circle is 5, and the radius is 2.5. Therefore, the area of the circle is:

(2.5)^2 x π = 6.25π

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Re: A 3 by 4 rectangle is inscribed in a circle. What is the area of the &nbs [#permalink] 27 Nov 2017, 10:50
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