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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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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. $$\frac{\sqrt{2}- 1}{2}$$

Attachment:

GEOMETRY 6.JPG [ 9.99 KiB | Viewed 11207 times ]
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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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04 Oct 2009, 15:24

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. $$\frac{\sqrt{2}- 1}{2}$$

R radius of big circle=1, r radius of inscribed circle.

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

$$R=1= r*\sqrt{2}+r$$ --> $$r=\frac{1}{(\sqrt{2}+1)}=\sqrt{2}-1$$

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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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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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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 ?

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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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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 ?

Look at the diagram:
Attachment:

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 $$BO+OD=r*\sqrt{2}+r=1$$ --> $$r=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1$$

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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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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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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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26 Feb 2020, 13:42
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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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