If `D` is the mid-point of the side `B C` of triangle `A B C` and `A D` is perpendicular to `A C` , then `3b^2=a^2-c`^2 (b) `3a^2=b^2 3c^2` `b^2=a^2-c^2` (d) `a^2+b^2=5c^2`

Explanation

With the given details, we can create a diagram.

Please refer to video to see the diagram.

From, the diagram,

`cos C = b/(a/2) = (2b)/a`

`=>(a^2+b^2-c^2)/(2ab) = (2b)/a`

`=>a^2+b^2-c^2 = 4b^2`

`=>a^2-c^2 = 3b^2`

So, option `(a)` is the correct option.