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Difference between revisions of "2009 IMO Problems/Problem 4"

(Created page with '== Problem == Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle BAC</math> meet the sides <math>BC</mat…')
 
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== Problem ==
 
== Problem ==
  
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Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle BAC</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 incentre of triangle <math>ADC</math>. Suppose that <math>\angle BEK=45^\circ</math>. Find all possible values of <math>\angle CAB</math>.  
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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 incentre 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''
  
 
--[[User:Bugi|Bugi]] 10:27, 23 July 2009 (UTC)Bugi
 
--[[User:Bugi|Bugi]] 10:27, 23 July 2009 (UTC)Bugi

Revision as of 01:36, 10 July 2012

Problem

Let $ABC$ be a triangle with $AB=AC$. The angle bisectors of $\angle CAB$ and $\angle ABC$ meet the sides $BC$ and $CA$ at $D$ and $E$, respectively. Let $K$ be the incentre of triangle $ADC$. Suppose that $\angle BEK=45^\circ$. Find all possible values of $\angle CAB$.

Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea

--Bugi 10:27, 23 July 2009 (UTC)Bugi

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