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Grade 12th passVectors

if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

PRASHANT KUMAR

12 Years agoGrade 12th pass

1 Answer

Satyajit Samal

11 Years ago

The correct question is $AB+AD+CB+CD=4EF$
Since F is the midpoint of BD, we get $AB+AD = 2AF$ …...(1)
Similarly $CB+CD = 2 CF$ …....(2)
Adding (1) and (2) we get $AB+AD+CB+CD=2\left ( AF+CF \right ) \\ \Rightarrow AB+AD+CB+CD = -2\left ( FA+FC \right ) \\ \Rightarrow AB+AD+CB+CD = -2 \left ( 2FE \right ) \\ \RIghtarrow AB+AD+CB+CD = 4EF$
Hence proved.

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