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If ABC is a quarter circle and a circle is inscribed in it and if AB=

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If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 02 Oct 2009, 08:47
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If ABC is a quarter circle and a circle is inscribed in it and if AB= 1 cm, find radius of inner circle.


A. \(\sqrt{2}- 1\)

B. \(\frac{\sqrt{2}+1}{2}\)

C. \(\frac{\sqrt{2}- 1}{2}\)

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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 01 Nov 2010, 02:03
Bunuel, could you please explain this:

Quote:
R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1
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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 24 Dec 2010, 07:59
Bunuel wrote:
R radius of big circle=1, r radius of inscribed circle.

Diagonal of a square made of r=r*\sqrt{2}

R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

A.


Colud not understand this.. can someone help ?

thanks in advance
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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 24 Dec 2010, 08:22
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nonameee wrote:
Bunuel, could you please explain this:

Quote:
R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

hirendhanak wrote:
Bunuel wrote:
R radius of big circle=1, r radius of inscribed circle.

Diagonal of a square made of r=r*\sqrt{2}

R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

A.


Colud not understand this.. can someone help ?

thanks in advance


Look at the diagram:
Attachment:
GEOMETRY 6.PNG
GEOMETRY 6.PNG [ 11.76 KiB | Viewed 8543 times ]
Diagonal BO of the square made by the radii of the small circle equals to \(BO=\sqrt{r^2+r^2}=r*\sqrt{2}\);

Now, the radius of the big circle BD equals to \(BO+OD=r*\sqrt{2}+r=1\) --> \(r=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1\)

Answer: A.
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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 25 Dec 2010, 09:35
Nice explanation.
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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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New post 25 Dec 2010, 15:53
Oh this one was tough.
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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=  [#permalink]

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Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=   [#permalink] 26 Feb 2020, 13:42
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