KöMaL 2017 K566

The lengths of the sides of a quadrilateral $ABCD$ are $AB = 8$ cm, $BC= 7$ cm, $CD = 6$ cm and $DA = 5$ cm. The inscribed circles of triangles $BCD$ and $ABD$ touch diagonal $BD$ at points $E$ and $F$, respectively. What is the length of the line segment $EF$?