If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three vectors such that $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi}{2}$,then:

• A
  $a^2=b^2+c^2$
• B
  $b^2=c^2+a^2$
• C
  $c^2=a^2+b^2$
• D
  $2 a^2-b^2=c^2$