Chords and of a circle intersect at a point inside the circle. Let be an interior point of the segment . The tangent line at to the circle through , , and intersects the lines and at and , respectively. If find in terms of .
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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 $t$.
Izvor: Međunarodna matematička olimpijada, shortlist 1990
Školjka 
and 
of a circle intersect at a point 
inside the circle. Let 
be an interior point of the segment 
. The tangent line at 
, 
and 
at 
and 
, respectively. If
in terms of 
.