ABCD is a trapezium with ADBC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =

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Solution

Q.
ABCD is a trapezium with AD $∥$ BC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =

1 6 cm

2 7 cm

3 8 cm

4 9 cm

Ans.
(3)

$A D ∥ B C$

and $\frac{A O}{O C} = \frac{D O}{O B} = \frac{1}{2}$

$∴$ $\frac{A D}{B C} = \frac{A O}{O C} \Rightarrow \frac{4}{B C} = \frac{1}{2} \Rightarrow B C = 8 cm$

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