BdMO National 2013: Junior 3

[BdMO]

$ABC$ 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]

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