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.D M+``((B C)/2)^2`
(ii) `A B^2=A D^2-B CdotD M+``((B C)/2)^2`
(iii) `A C^2+A B^2=2A D^2+``1/2B C^2`

Explanation

Given:


In `∆ABC, AD `is a median, `AM ⊥ BC.`


To Prove


...