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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− | Let <math>ABC</math> be a triangle with <math>AB=AC</math>. The angle bisectors of <math>\angle CAB</math> and <math>\angle | + | 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 02:36, 10 July 2012
Problem
Let be a triangle with
. The angle bisectors of
and
meet the sides
and
at
and
, respectively. Let
be the incentre of triangle
. Suppose that
. Find all possible values of
.
Authors: Jan Vonk and Peter Vandendriessche, Belgium, and Hojoo Lee, South Korea
--Bugi 10:27, 23 July 2009 (UTC)Bugi