Question

In the given figure, DE || AC and DC || AP, such that BC = 4 cm and BP = 6 cm, then $\frac{BE}{EC}$ is equal to

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 3

Answer 1

The correct option is C

2 : 1

$DE||AC$
$\Rightarrow \frac{BE}{EC}=\frac{BD}{DA}$ ...(i)
Also, in $\Delta BAP$,
$\frac{BC}{CP}=\frac{BD}{DA}$ ...(ii)
From Eqs. (i) and (ii), we get
$\frac{BE}{EC}=\frac{BC}{CP}$
$\Rightarrow \frac{BE}{EC}=\frac{BC}{BP-BC}$
$\Rightarrow \frac{BE}{EC}=\frac{4}{6-4}=\frac{2}{1}$ [given: BC = 4 cm and BP = 6 cm]