If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid\overrightarrow{a}\mid$ then show that vector $(2\overrightarrow{a}+\overrightarrow{b})$ is perpendicular to $\overrightarrow{b}$.

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