Let $O$ is the center of the circumcircle of the triangle $ABC$. We know that $AB =1$ and $AO = AC = 2$ . Points $D$ and $E$ lie on extensions of sides $AB$ and $AC$ beyond points $B$ and $C$ respectively such that $OD = OE$ and $BD =\sqrt2 EC$. Find $OD^2$.
Problem
Source: December 2020 Ukraine Geometry Olympiad VIII p5 , IX p4
Tags: geometry, Circumcenter, equal segments