IGO 2016 A3

In a convex qualrilateral $ABCD$ , let $P$ be the intersection point of $AD$ and $BC$ . Suppose that $I_1$ and $I_2$ are the incenters of triangles $PAB$ and $PDC$ ,respectively. Let $O$ be the circumcenter of $PAB$ , and $H$ the orthocenter of $PDC$ . Show that the circumcircles of triangles $AI_1B$ and $DHC$ are tangent together if and only if the circumcircles of triangles $AOB$ and $DI_2C$ are tangent together. Proposed by Hooman Fattahimoghaddam