For an acute triangle $ABC$, let $O$ be its circumcenter, and let $O_A,O_B,O_C$ be the circumcenter of $BCO,CAO,ABO$ respectively. Show that $AO_A,BO_B,CO_C$ are concurrent.
Source: Dürer Competition Finals 2023/E+ 5
Tags: geometry, circumcircle
For an acute triangle $ABC$, let $O$ be its circumcenter, and let $O_A,O_B,O_C$ be the circumcenter of $BCO,CAO,ABO$ respectively. Show that $AO_A,BO_B,CO_C$ are concurrent.