Question

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

विकल्प

• 6 cm

• 7 cm

• 8 cm

• 9 cm

Answer 1

ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB = 1/2, then BC = 8 cm.

Explanation:

In ΔAOD and ΔBOC

∠AOD = ∠BOC  .....(Vertically opposite angle)

`(AO)/(OC) = (DO)/(OB)`  ......(Given)

∴ ΔAOD ∼ΔBOC  ......(SAS similarity)

Since both triangles are similar.

Their sides will be in proportion

`(AO)/(OC) = (DO)/(OB) = (AD)/(BC)`

`1/2 = (AD)/(BC)`

Putting AD = 4 cm

`1/2 = 4/(BC)`

BC = 2 × 4

BC = 8 cm