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2

Part of 2013 Gulf Math Olympiad

Problems(1)

Gulf Mathematical Olympiad 2013 - Problem 2

Source: Gulf Mathematical Olympiad 2013

4/5/2013
In triangle ABCABC, the bisector of angle BB meets the opposite side ACAC at B′B'. Similarly, the bisector of angle CC meets the opposite side ABAB at C′C' . Prove that A=60∘A=60^{\circ} if, and only if, BC′+CB′=BCBC'+CB'=BC.
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