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In figure, Ad is a median of a triang...

In figure, Ad is a median of a triangle ABC and `A M_|_B C` . Prove that: (i) `A C^2=A D^2+B C""""dot""""D M""+` `((B C)/2)^2` (ii) `A B^2=A D^2-B C""""dot""""D M""+` `((B C)/2)^2` (iii) `A C^2+A B^2=2A D^2+` `1/2B C^2`

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