# ABCD is a trapezium whose BC parallel AD and AD = 4 cm. Diagonals AC and BD are intersected at O in such way that [AO]/[OC] = [DO]/[OB] = 1/2, then what is the length of BC?

Dec 25, 2016

$B C = 8$

#### Explanation:

Given $B C$ parallel to $A D , \mathmr{and} A D = 4$
Let $B C = m$
Let $\angle A O D = x , \implies \angle C O B = x$
Let $\angle O A D = y , \implies \angle O C B = y$
Let $C O = 2 a , \implies O A = 1 a$

$\implies \Delta O A D , \mathmr{and} \Delta O C B$ are similar,
$\implies \frac{O A}{A D} = \frac{O C}{C B}$
$\implies \frac{1 a}{4} = \frac{2 a}{m}$
$\implies m = 8$

Hence, $B C = m = 8$