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From a point `O` in the interior of a ` A B C` , perpendiculars `O D ,\ O E` and `O F` are drawn to the sides `B C ,\ C A` and `A B` respectively. Prove that: (i) `A F^2+B D^2+C E^2=O A^2+O B^2+O C^2-O D^2-O E^2-O F^2` (ii) `A F^2+B D^2+C E^2=A E^2+C D^2+B F^2`

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