CN-TST 2014 Problem 13

Let the circumcenter of triangle $ABC$ be $O$ . $H_A$ 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 circumcentre 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