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# Consider a quarter of a circle of radius 16. Let r be the radius of th

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Joined: 23 Oct 2011
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Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

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21 Apr 2012, 09:28
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Difficulty:

65% (hard)

Question Stats:

58% (02:34) correct 42% (02:24) wrong based on 144 sessions

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Consider a quarter of a circle of radius 16. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

A. $$16*(\sqrt{2} -1)$$

B. $$8*(\sqrt{3} -1)$$

C. $$4*(\sqrt{7} - 1)$$

D. $$12* (\sqrt{7} -1)$$

E. None of these

A question from MBA Strategy course
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Joined: 02 Sep 2009
Posts: 53063
Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

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21 Apr 2012, 11:09
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JubtaGubar wrote:
Consider a quarter of a circle of radius 16. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

A. $$16*(\sqrt{2} -1)$$

B. $$8*(\sqrt{3} -1)$$

C. $$4*(\sqrt{7} - 1)$$

D. $$12* (\sqrt{7} -1)$$

E. None of these

A question from MBA Strategy course

Look at the diagram below:
Attachment:

Quarter of circle.png [ 5.62 KiB | Viewed 5707 times ]

The radius of a quarter of a circle equals to the diagonal of a square made by the radii of the inscribed circle plus the radius of that circle.

Now, since the sides of a square equal to $$r$$, then its diagonal equals to $$r\sqrt{2}$$, hence $$r\sqrt{2}+r=16$$ --> $$r=\frac{16}{\sqrt{2}+1}$$.

Rationalise by multiplying both numerator and denominator by $$\sqrt{2}-1$$: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}$$ --> apply $$(a+b)(a-b)=a^2-b^2$$ to the expression in the denominator: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{16(\sqrt{2}-1)}{2-1}=16(\sqrt{2}-1)$$.

Hope it's clear.
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Intern
Joined: 23 Oct 2011
Posts: 43
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Re: Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

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23 Apr 2012, 07:13
Thank you Bunuel!

I got 16/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
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Re: Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

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30 Jan 2019, 01:04
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30 Jan 2019, 01:10
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Re: A circle is inscribed in a quadrant of a circle of radius 1   [#permalink] 30 Jan 2019, 01:10
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