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2006 IMO Problems/Problem 1

Revision as of 22:11, 22 May 2014 by Swamih (talk | contribs) (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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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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