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AD, BE and CF are the medians of triangl...

AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that `2a^(2) = b^(2) + c^(2)`

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Points A, F, G and E are concylic,

`rArr BG. BE = BF.BA`
`rArr (2)/(3) (BE)^(2) = (1)/(2) c^(2)`
`rArr (2)/(3) xx (1)/(4) (2a^(2) + 2c^(2) -b^(2)) = (1)/(2) c^(2)` (Using Apollonius Theorem)
`rArr 2a^(2) = b^(2) + c^(2)`
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