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If a rectangle with a diagonal of 5 inches is inscribed in circle O, w

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Math Expert
Joined: 02 Sep 2009
Posts: 55618
If a rectangle with a diagonal of 5 inches is inscribed in circle O, w  [#permalink]

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10 Jan 2019, 03:04
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25% (medium)

Question Stats:

95% (00:47) correct 5% (00:22) wrong based on 25 sessions

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If a rectangle with a diagonal of 5 inches is inscribed in circle O, what is the circumference of circle O, in inches?

A. 5

B. $$\frac{5\pi}{2}$$

C. $$5\pi$$

D. $$6\pi$$

E. $$10\pi$$

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Joined: 10 Feb 2018
Posts: 33
GMAT 1: 550 Q46 V20
Re: If a rectangle with a diagonal of 5 inches is inscribed in circle O, w  [#permalink]

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10 Jan 2019, 03:26
Diagonal of rectangle would equal the diameter of circle.
Therefore the radius of circle would be 5/2
hence the circumference is 2*5/2*(pi)=5pi
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Re: If a rectangle with a diagonal of 5 inches is inscribed in circle O, w  [#permalink]

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10 Jan 2019, 07:02

Solution

Given:
A rectangle is inscribed in a circle with center O
• Diagonal length of the rectangle = 5 inches

To find:
• Circumference of the circle

Approach and Working:
Length of diagonal = length of the diameter of circle
• Thus, diameter = 5 => radius = $$\frac{5}{2}$$

Therefore, circumference of the circle = $$2ᴨr = 2 * ᴨ * \frac{5}{2} = 5ᴨ$$

Hence, the correct answer is Option C

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Re: If a rectangle with a diagonal of 5 inches is inscribed in circle O, w  [#permalink]

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10 Jan 2019, 07:12
IMO C

Right angle in a circle indicates that diagonal is the diameter

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Re: If a rectangle with a diagonal of 5 inches is inscribed in circle O, w  [#permalink]

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10 Jan 2019, 07:26
Bunuel wrote:
If a rectangle with a diagonal of 5 inches is inscribed in circle O, what is the circumference of circle O, in inches?

A. 5

B. $$\frac{5\pi}{2}$$

C. $$5\pi$$

D. $$6\pi$$

E. $$10\pi$$

diagonal = diameter
so
circumference = 2* pi * 2.5
IMO C 5 pi
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Re: If a rectangle with a diagonal of 5 inches is inscribed in circle O, w   [#permalink] 10 Jan 2019, 07:26
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