BG-MO 1988 Problem 4

Let $A,B,C$ be non-collinear points. For each point $D$ of the ray $AC$ , we denote by $E$ and $F$ the points of tangency of the incircle of $\triangle ABD$ with $AB$ and $AD$ , respectively. Prove that, as point $D$ moves along the ray $AC$ , the line $EF$ passes through a fixed point.