In a triangle $$ABC$$, $$a$$, $$b$$, $$c$$ denote the lengths of the sides $$BC$$, $$CA$$, $$AB$$. If $$D$$ is the midpoint of the side $$BC$$ and $$AD$$ is perpendicular to $$AC$$, then

A

$$3b^2 = a^2 - c^2$$

B

$$3a^2 = b^2 - 3c^2$$

C

$$b^2 = a^2 - c^2$$

D

$$a^2 + b^2 = 5c^2$$

E

none of these