ELMO 2016 Problem 2

Oscar is drawing diagrams with trash can lids and sticks. He draws a triangle $ABC$ and a point $D$ such that $DB$ and $DC$ are tangent to the circumcircle of $ABC$ . Let $B'$ be the reflection of $B$ over $AC$ and $C'$ be the reflection of $C$ over $AB$ . If $O$ is the circumcenter of $DB'C'$ , help Oscar prove that $AO$ is perpendicular to $BC$ .

James Lin