We have a triangle with side lengths $a$ = $345678$, $b$ = $456784$ and $c$ = $567890$ with vertices named $A$, $B$ and $C$, and $I$ denote the incentre of circle. Line segment $BI$ is extended to meet opposite side of triangle ie. $AC$ at $K$. Find length of line segment $IK$.

Note : $a$ is side opposite to vertex $A$, $b$ is opposite to vertex $B$ and $c$ is opposite to vertex $C$.