Could you find the radius?

Point $K$ belongs to base $AD$ of trapezoid $ABCD$ . It is known that $AB = BK, KC = CD$ and the areas of triangles $ABK$ and $KCD$ are in the ratio of $5$ . The radii of the incircles of triangles $ABK$ and $KCD$ are equal to $5$ and $2$ respectively.

Find the radius of the incircle of triangle $KBC$ .