USAMO 2020 — Days 1 and 2 Question 1

An acute triangle $ABC$ is inscribed in circle $\omega$ with center $O$. A variable point $X$ lies on the minor arc $AB$, and $CX$ meets $AB$ at $D$. Let $O_1,O_2$ be the circumcenters of $ADX,BDX$. Determine all $X$ minimizing $[OO_1O_2]$.

Proposed by Zuming Feng. Source: Evan Chen’s third-party solution notes.

Source video link: https://youtu.be/r7j0oRtpErA?t=2070