1990 IMO Problems/Problem 1

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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 $t$.

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