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A point D is taken on the side B C of a ...

A point `D` is taken on the side `B C` of a ` A B C` such that `B D=2d Cdot` Prove that `a r( A B D)=2 ar( A D C)dot`

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Proof:
In` /_\ABC, BD=2DC`
Let `E` be the mid point of `BD`.
`:.BE=ED=DC`
Since`AE` and `AD` are medians of `/_\ABD` and `/_\ AEC` respectively
`:.ar(ABD)=2ar(AED)` and `ar(ADC)=ar(AED)`
`=>ar (ABD)=2ar(ADC)`
Hence Proved.
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