Difference between revisions of "2009 IMO Problems/Problem 4"
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== Problem == | == Problem == | ||
| − | Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle ABC</math> meet the sides <math>BC</math> and <math>CA</math> at <math>D</math> and <math>E</math>, respectively. Let <math>K</math> be the | + | Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle ABC</math> meet the sides <math>BC</math> and <math>CA</math> at <math>D</math> and <math>E</math>, respectively. Let <math>K</math> be the incenter of triangle <math>ADC</math>. Suppose that <math>\angle BEK=45^\circ</math>. Find all possible values of <math>\angle CAB</math>. |
''Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea'' | ''Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea'' | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2009|num-b=3|num-a=5}} | ||
Latest revision as of 11:53, 30 June 2024
Problem
Let 
be a triangle with 
. The angle bisectors of 
and 
meet the sides 
and 
at 
and 
, respectively. Let 
be the incenter of triangle 
. Suppose that 
. Find all possible values of .
Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2009 IMO (Problems) • Resources | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
| All IMO Problems and Solutions | ||
