HMMT 2016 G9

In cyclic quadrilateral $A B C D$ with $A B=A D=49$ and $A C=73$, let $I$ and $J$ denote the incenters of triangles $A B D$ and $C B D$. If diagonal $\overline{B D}$ bisects $\overline{I J}$, find the length of $I J$.