Question

$\text{In the given figure,}DE||AC,DC||AP,BC=4\text{cm,}\text{and}BP=6\text{cm}.$

$\text{Find the value of}\frac{BE}{EC}.$

Answer 1

$\text{Given:}DE||AC.$

$\text{Applying BPT to}△BAC\text{we get}$,

$\frac{BE}{EC}=\frac{BD}{DA}\cdots \left(i\right)$

$\text{Also, it is given that}DC||AP.$

$\text{Applying BPT to}△BAP\text{we get}$,

$\frac{BC}{CP}=\frac{BD}{DA}\cdots \left(ii\right)$

$\text{From (i) and (ii), we get}\frac{BE}{EC}=\frac{BC}{CP}$

$\text{We know that, CP = BP - BC}$
$\Rightarrow \frac{BE}{EC}=\frac{BC}{BP-BC}$

$\text{Given:}BC=4\text{cm}$ and $BP=6\text{cm}$.
$\Rightarrow \frac{BE}{EC}=\frac{4}{6-4}=\frac{2}{1}$

$\therefore BE:EC=2:1$