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Omni-MATH / 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 interse…

Problem

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problem

Chords AB AB and CD CD of a circle intersect at a point E E inside the circle. Let M M be an interior point of the segment EB EB. The tangent line at E E to the circle through D D, E E, and M M intersects the lines BC BC and AC AC at F F and G G, respectively. If \[ \frac {AM}{AB} \equal{} t, \] find EGEF\frac {EG}{EF} in terms of t t.
Plain-text mathematical notation (without MathML)
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
\[ \frac {AM}{AB} \equal{} t,
\]
find (EG)/(EF) in terms of t.
Original LaTeX notation
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
\[ \frac {AM}{AB} \equal{} t,
\]
find $\frac {EG}{EF}$ in terms of $ t$.

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Source and history

task_id
d183f171-250b-5eec-85cd-d2d9a5498b87
task_key
test--d183f171-250b-5eec-85cd-d2d9a5498b87
task_revision_id
1
config / split
/ test

Official source

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