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A B C D is a parallelogram and E is the ...

`A B C D` is a parallelogram and `E` is the mid-point of `B C , DE and AB` when produced meet at `F` Then `A F=`
(a) `3/2 AB`
(b) `2 AB`
(c) `3 AB`
(d)`5/4 AB`

Text Solution

Verified by Experts

`/_\DCE \and\BFE,DEC=BEF`(vertically opp any)
`EC=BE`(E is the mid point
`/_DCB=/_EBF` (alternate angle DC parallel to AF)
So`/_\ DCE= /_\BFE`
`DC=BF`(1)
`CD=AB` (ABCD is a parallelogram
`AF=AB+BF`
`(AB+DC)` from (1)
`=AB+AB=2AB`
So option(b) is Correct.
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