Question 99
Let $O$ be the circumcenter of triangle $ABC$. $H_A$ is the projection of $A$ onto $BC$. The extension of $AO$ intersects the circumcircle of $BOC$ at $A'$. The projections of $A'$ onto $AB$, $AC$ are $D$, $E$, and $O_A$ is the circumcenter of triangle $DH_AE$. Define $H_B, O_B, H_C, O_C$ similarly.
Prove: $H_AO_A$, $H_BO_B$, $H_CO_C$ are concurrent.
Prove: $H_AO_A$, $H_BO_B$, $H_CO_C$ are concurrent.