Let the arc AC of a circle subtend a right angle at the centre O . If the point B on the $\operatorname{arc}\text{AC}$, divides the arc AC such that $\frac{{\text{ length of }\operatorname{arcAB}}}{{\text{ length of }\operatorname{arc}\text{BC}}}=\frac{1}{5}$, and $\overrightarrow{{\text{OC}}}=\alpha \overrightarrow{{\text{OA}}}+\beta \overrightarrow{{\text{OB}}}$, then $\alpha +\sqrt{2}(\sqrt{3}-1)\beta $ is equal to