31st Junior Turkish Mathematical Olympiad

Let $ABCD$ be a cyclic quadrilateral and let the incenters of the triangles $BAD$ and $CAD$ be $I$ and $J$, respectively. Let the intersection point of the line that passes through $I$ and perpendicular to $BD$ and the line that passes through $J$ and perpendicular to $AC$ be $K$. Prove that $KI=KJ$.