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Question

Diagonals AC and BD of a trapezium ABCD with AB DC intersect each other at O.then, ar (AOD) = ___.


A

Area (BOC)

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B

Area (AOD)

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C

Area (BOD)

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D

None of the above

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Solution

The correct option is A

Area (BOC)


It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.

∴ Area (ΔDAC) = Area (ΔDBC)

⇒ Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)

⇒ Area (ΔAOD) = Area (ΔBOC)


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