let $O$ be the centre of the circle through the points $A,B,C$.Let $D$be the mid point of $AB$.Let $E$ be the centroid of the triangle $ACD$.Prove that, the line $CD$ will be perpendicular to the line $OE$ iff $AB=AC$
the book provides the solution in vector could someone do it in the geometric way?
$7777^{th}$
Second Balkan Mathematical Olympiad
- nafistiham
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Last edited by nafistiham on Mon Jan 23, 2012 6:23 pm, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Second Balkan Mathematical Olympiad
প্রশ্নই তো অসম্পূর্ণ মনে হচ্ছে!!!
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- nafistiham
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Re: Second Balkan Mathematical Olympiad
sorry.nafistiham wrote:Prove that, the line $CD$ will be perpendicular to the line $OE$ iff $AB+AC$
it should have been like this.
nafistiham wrote:Prove that, the line $CD$ will be perpendicular to the line $OE$ iff $AB=AC$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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- Phlembac Adib Hasan
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Re: Second Balkan Mathematical Olympiad
My Proof :
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- nafistiham
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Re: Second Balkan Mathematical Olympiad
thanks for the nice proof. (and i am uploading the figure as a jpeg file, so that none has to download it. )
$400^{th}$\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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