1990 IMO Problems/Problem 1

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 $\overline{EB}$ . The tangent line at $E$ to the circle through $D, E$ , and $M$ intersects the lines $\overline{BC}$ and ${AC}$ at $F$ and $G$ , respectively. If $\frac{AM}{AB} = t$ , find $\frac{EG}{EF}$ in terms of $t$ .