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2009 IMO Problems/Problem 4

Revision as of 06:27, 23 July 2009 by Bugi (talk | contribs) (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

Let $ABC$ be a triangle with $AB=AC$. The angle bisectors of $\angle CAB$ and $\angle BAC$ 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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