IMO Shortlist 1990 problem 11
Dodao/la:
arhiva2. travnja 2012. 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
.
%V0
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 
