BdMO National 2013: Junior 3

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

BdMO National 2013: Junior 3

Unread post by BdMO » Fri Jan 10, 2014 1:23 am

$ABC$ is a triangle where $AN$ is perpendicular to $CB$ and $BM$ perpendicular to $AC$. The length of $BC$ is $10$, that of $AC$ is $12$ and that of $AN$ is $6$. Find the length of $BM$.

Tahmid
Posts: 110
Joined: Wed Mar 20, 2013 10:50 pm

Re: BdMO National 2013: Junior 3

Unread post by Tahmid » Sat Jan 11, 2014 10:49 pm

$\Delta ANC\sim \Delta BMC$
$\frac{AN}{BM}=\frac{AC}{BC}$
$\frac{6}{BM}=\frac{12}{10}$
$BM=\frac{6*10}{12}=\frac{60}{12}=5$
$BM=5 \left ( ans: \right )$....... :)

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