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Difference between revisions of "2006 IMO Problems/Problem 1"

(Created page with "==Problem== 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 P...")
 
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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>
  
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==Solution==.
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==Solution==
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Revision as of 23:12, 22 May 2014

Problem

Let $ABC$ be triangle with incenter $I$. A point $P$ in the interior of the triangle satisfies $\angle PBA+\angle PCA = \angle PBC+\angle PCB$. Show that $AP \geq AI$, and that equality holds if and only if $P=I$

Solution

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