MathNet 1996 — Part 01 Question 1

$ABC$ is acute-angled. $D$ is a variable point on the side $BC$. $O_1$ is the circumcenter of $ABD$, $O_2$ is the circumcenter of $ACD$, and $O$ is the circumcenter of $AO_1O_2$. Find the locus of $O$.