Difference between revisions of "1990 IMO Problems/Problem 1"
(Created page with "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 EB. The tangent line at E to the circle through D, E, and M...") |
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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 EB. The tangent line at E to the circle | + | 1. Chords <math>AB</math> and <math>CD</math> of a circle intersect at a point <math>E</math> inside the circle. Let <math>M</math> be an interior point of the segment <math>\overline{EB}</math>. The tangent line at <math>E</math> to the circle through <math>D, E</math>, and <math>M</math> intersects the lines <math>\overline{BC}</math> and <math>{AC}</math> at <math>F</math> and <math>G</math>, respectively. |
| − | through D, E, and M intersects the lines BC and AC at F and G, respectively. | + | If <math>\frac{AM}{AB} = t</math>, find <math>\frac{EG}{EF}</math> in terms of <math>t</math>. |
| − | If <math>\frac{AM}{AB} = t</math>, find | ||
Revision as of 05:42, 5 July 2016
1. 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 
.
