In a triangle $ABC,$ points $M$ and $N$ are on sides $AB$ and $AC$, respectively,
such that $MB = BC = CN$. Let $R$ and $r$ denote the circumradius and the inradius of the
triangle $ABC$, respectively. Express the ratio $\frac {MN}{BC}$ in terms of $R$ and $r$.
APMO 2005-5
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nafistiham
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\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Sazid Akhter Turzo
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Re: APMO 2005-5
I think in the last line, it's $\frac{MN}{BC}$ , not $MN=BC$.
Turzo
Turzo
Re: APMO 2005-5
Edited the typo.
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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nafistiham
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Re: APMO 2005-5
I actually copied from the .pdf. so....\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.