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Weird angle is 30 degrees

Source: 2020 China North Mathematical Olympiad Advanced Level P2

August 4, 2020
geometryCircumcenterincenter

Problem Statement

In △ABC\triangle ABC, AB>ACAB>AC. Let OO and II be the circumcenter and incenter respectively. Prove that if ∠AIO=30∘\angle AIO = 30^{\circ}, then ∠ABC=60∘\angle ABC = 60^{\circ}.
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