Difference between revisions of "1997 IMO Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | The angle at <math>A</math> is the smallest angle of triangle <math> | + | The angle at <math>A</math> is the smallest angle of triangle <math>ABC</math>. The points <math>B</math> and <math>C</math> divide the circumcircle of the triangle into two arcs. Let <math>U</math> be an interior point of the arc between <math>B</math> and <math>C</math> which does not contain <math>A</math>. The perpendicular bisectors of <math>AB</math> and <math>AC</math> meet the line <math>AU</math> and <math>V</math> and <math>W</math>, respectively. The lines <math>BV</math> and <math>CW</math> meet at <math>T</math>. Show that. |
<math>AU=TB+TC</math> | <math>AU=TB+TC</math> | ||
| − | |||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1997|num-b=1|num-a=3}} | ||
| + | [[Category:Olympiad Geometry Problems]] | ||
| + | [[Category:3D Geometry Problems]] | ||
Latest revision as of 22:58, 28 March 2024
Problem
The angle at 
is the smallest angle of triangle 
. The points 
and 
divide the circumcircle of the triangle into two arcs. Let 
be an interior point of the arc between and which does not contain . The perpendicular bisectors of 
and 
meet the line 
and 
and 
, respectively. The lines 
and 
meet at 
. Show that.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1997 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
