Question 65
Let $O$ be the circumcenter of the triangle $\triangle ABC$. Let $D, E$ on $AC, AB$ and $P, Q, R, S$ be points such that $P, C$ and $R, C$ lie on the different sides of $AB$, $Q, B$ and $S, B$ lie on the different sides of $AC$ and $R, S$ lie on circumcircle of $\triangle DAP$, $\triangle EAQ$. We have $\triangle BCE \sim \triangle ADQ$, $\triangle CBD \sim \triangle AEP$ (In that order) and $\angle ARE = \angle ASD = \angle BAC$. If $RS \parallel PQ$, prove that $RE, DS$ intersect on $AO$.