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705-805 (Hard)|   Geometry|      
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virtualanimosity
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If ABC is a quarter circle and a circle is inscribed in it and if AB= 02 Oct 2009, 09:47
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85% (hard)

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52% (02:36) correct 48% (02:23) wrong based on 86 sessions

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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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If ABC is a quarter circle and a circle is inscribed in it and if AB= 24 Dec 2010, 09:22
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nonameee
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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hirendhanak
Bunuel
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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GEOMETRY 6.PNG [ 11.76 KiB | Viewed 13291 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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If ABC is a quarter circle and a circle is inscribed in it and if AB= 04 Oct 2009, 16:24
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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. \(\frac{\sqrt{2}- 1}{2}\)


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

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

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

Answer: A.
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If ABC is a quarter circle and a circle is inscribed in it and if AB= 01 Nov 2010, 03:03
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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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If ABC is a quarter circle and a circle is inscribed in it and if AB= 24 Dec 2010, 08:59
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Bunuel
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.
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Colud not understand this.. can someone help ?

thanks in advance
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If ABC is a quarter circle and a circle is inscribed in it and if AB= 25 Dec 2010, 10:35
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Nice explanation.
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If ABC is a quarter circle and a circle is inscribed in it and if AB= 19 Jan 2026, 10:52
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