IMO 1990 Problem 1

Chords $AB$ and $CD$ of a circle intersect at a point $E$ inside the circle. Let $M$ be an interior point of the segment $EB$ . The tangent line at $E$ to the circle through $D$ , $E$ , and $M$ intersects the lines $BC$ and $AC$ at $F$ and $G$ , respectively. If $$\frac {AM}{AB} = t,$$ find $\frac {EG}{EF}$ in terms of $t$ .