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Question

In the given figure, ABCD is a quadrilateral in which diagonals AC and BD intersect at a point E then,

A
Area ΔAED×Area ΔBEC=Area ΔABE×Area ΔCDE
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B
Area ΔABE×Area ΔBEC=Area ΔAED×Area ΔCDE
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C
Area ΔBEC×Area ΔCDE=Area ΔAED×Area ΔABE
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D
None of these
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Solution

The correct option is A Area ΔAED×Area ΔBEC=Area ΔABE×Area ΔCDE
Draw AMBD and CNBD
Area ΔAED×area ΔBEC
=(12ED×AM)×(12BE×CN)
=14ED×AM×BE×CN
=(12BE×AM)×(12DE×CN)
=area ΔABE×area ΔCDE

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