2021 IIMC keystage3-IWYMIC team Question 3

Let $ABC$ be a triangle and $O$ be a point in its interior such that $\angle ABO=\angle CAO$, $\angle BAO=\angle BCO$ and $\angle BOC=90^\circ$, as shown in the diagram below. If $AC=2$ cm, then find the length, in cm, of $OC$.