Dhaka Junior 2011/9
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Please don't post problems (by starting a topic) in the "Junior: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
9. $ABC$ is a triangle with $AB = 4$, $BC = 5$ and $AC = 3$. $O$ is the midpoint of $BC$. A line from $O$ parallel to $AC$ meets $AB$ at $D$. $E$ is on $DO$ so that $DO = OE$ and $D$ and $E$ are on opposite sides of $BC$. Find $BE^2$.
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Re: Dhaka Junior 2011/9
How can we get the answer [13]?
Re: Dhaka Junior 2011/9
May be BE=DC.
(BOE and DOC is similar)
DC^2=OC^2-OD^2=2.5^2-1.5^2=4
(BOE and DOC is similar)
DC^2=OC^2-OD^2=2.5^2-1.5^2=4
- nafistiham
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Re: Dhaka Junior 2011/9
$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Dhaka Junior 2011/9
Can u draw it on a paper and then upload the image with positions of all e points? I cant understand the position of enafistiham wrote:$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
- nafistiham
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Re: Dhaka Junior 2011/9
Sorry for being so late.Shafin wrote:Can u draw it on a paper and then upload the image with positions of all e points? I cant understand the position of enafistiham wrote:$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
here is what you wanted.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.