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प्रश्न
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
उत्तर
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
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