Question 4
Right triangle $ABC$ has $\angle A=90^\circ$, $AB=30$ and $AC=40$. Its incircle, with centre $I$, touches $BC$ at $K$. A point $M$ on segment $KC$ is chosen so that line $AM$ meets the incircle at $E$ and $F$, in that order, and $AE=MF$. Find $EF$.
