2006 IMO Problems/Problem 1: Difference between revisions
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Let <math>ABC</math> be triangle with incenter <math>I</math>. A point <math>P</math> in the interior of the triangle satisfies <math>\angle PBA+\angle PCA = \angle PBC+\angle PCB</math>. Show that <math>AP \geq AI</math>, and that equality holds if and only if <math>P=I</math> | Let <math>ABC</math> be triangle with incenter <math>I</math>. A point <math>P</math> in the interior of the triangle satisfies <math>\angle PBA+\angle PCA = \angle PBC+\angle PCB</math>. Show that <math>AP \geq AI</math>, and that equality holds if and only if <math>P=I</math> | ||
==Solution==. | ==Solution== | ||
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Revision as of 22:12, 22 May 2014
Problem
Let 
be triangle with incenter 
. A point 
in the interior of the triangle satisfies 
. Show that 
, and that equality holds if and only if 
Solution
.
