Preparation Marathon

For discussing Olympiad Level Number Theory problems
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*Mahi*
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Re: Preparation Marathon

Unread post by *Mahi* » Sat Dec 31, 2011 11:49 am

There was a little glitch, so I edited that. Notice that there can be squares which are a little "inclined".
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Nadim Ul Abrar
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Re: Preparation Marathon

Unread post by Nadim Ul Abrar » Mon Jan 02, 2012 5:24 pm

Preparation Marathon: Round 2 (problem 6)

sol :
we know that

$d^2=R^2-2Rr$ ($d$ is distance of incenter and circumcenter ,$ R$ is circumradius and $r$ is inradius )

$d=\sqrt{10^2-2.10.5}=0$ so for this case the incenter and curcumcenter will be same point .

So that that triangle will be equilateral triangle . :D
$\frac{1}{0}$
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Re: Preparation Marathon

Unread post by *Mahi* » Mon Jan 02, 2012 7:01 pm

In general, $R \geq 2r$ with equality only when $a=b=c$.
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