Dhaka Junior 2011/9

Problem for Junior Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
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.
User avatar
Moon
Site Admin
Posts: 751
Joined: Tue Nov 02, 2010 7:52 pm
Location: Dhaka, Bangladesh
Contact:

Dhaka Junior 2011/9

Unread post by Moon » Wed Feb 02, 2011 8:27 am

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 $BE^2$.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

Mehfuj Zahir
Posts: 78
Joined: Thu Jan 20, 2011 10:46 am

Re: Dhaka Junior 2011/9

Unread post by Mehfuj Zahir » Wed Feb 02, 2011 11:31 am

Answer is 13

ahmedulkavi
Posts: 14
Joined: Tue Feb 01, 2011 11:20 am

Re: Dhaka Junior 2011/9

Unread post by ahmedulkavi » Wed Feb 02, 2011 1:55 pm

How can we get the answer [13]?

Mehfuj Zahir
Posts: 78
Joined: Thu Jan 20, 2011 10:46 am

Re: Dhaka Junior 2011/9

Unread post by Mehfuj Zahir » Wed Feb 02, 2011 2:47 pm

BE^2=AD^2+DE^2

jkisor
Posts: 6
Joined: Fri Jun 29, 2012 12:31 pm

Re: Dhaka Junior 2011/9

Unread post by jkisor » Wed Jul 11, 2012 8:56 am

:?: May be BE=DC.
(BOE and DOC is similar)
DC^2=OC^2-OD^2=2.5^2-1.5^2=4

User avatar
nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

Re: Dhaka Junior 2011/9

Unread post by nafistiham » Wed Aug 29, 2012 11:48 pm

$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

User avatar
Shafin
Posts: 6
Joined: Thu Dec 27, 2012 3:05 pm

Re: Dhaka Junior 2011/9

Unread post by Shafin » Thu Jan 10, 2013 5:10 pm

nafistiham wrote:$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
Can u draw it on a paper and then upload the image with positions of all e points? I cant understand the position of e

User avatar
nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

Re: Dhaka Junior 2011/9

Unread post by nafistiham » Fri Jan 25, 2013 12:56 pm

Shafin wrote:
nafistiham wrote:$BD=2$
$DE=DO+OE=DO+DO=AC=3$
$BE^2=BD^2+DE^2=13$
Can u draw it on a paper and then upload the image with positions of all e points? I cant understand the position of e
Sorry for being so late. :oops: :oops:
here is what you wanted.
junior 2011-9.png
there is something called 'extension' :p
junior 2011-9.png (18.07 KiB) Viewed 2060 times
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

Post Reply