If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are any three vectors such that $\overrightarrow a=\overrightarrow b+\overrightarrow c$ and $\overrightarrow b$ is $\perp$ to $\overrightarrow c$, then ?

Question

$\begin{array}{1 1} (a)\:\:a^2=b^2+c^2\:\:\qquad\:\:(b)\:\:b^2=c^2+a^2\:\:\qquad\:\:(c)\:\:c^2=a^2+b^2\:\:\qquad\:\:(d)\:\:2a^2-b^2=c^2 \end{array} $