2006 IMO Problems/Problem 1

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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2006 IMO Problems/Problem 1

Problem

Solution