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> | ||
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==Solution== | ==Solution== |
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
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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 |