Question

In the given figure, D is the mid-point of AB and $PC=\frac{1}{2}AP=3$ cm. If $AD=DB=4$ cm and $DE||BP$ , then find the length of AE.

Answer 1

Given∶ $\frac{1}{2}AP=3cm$
$\therefore AP=6cm$
D is mid-point and $DE||BP$
$\Rightarrow$ E is the mid-point of AP (Converse of mid-point theorem)
$\therefore AE=\frac{1}{2}AP=\frac{1}{2}\times 6=3cm$
Hence, $AE=3cm$