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an acute angled triangle with $\angle{BAC}=60^0$

Source: APMO 2007

March 31, 2007
geometryincenter

Problem Statement

Let ABCABC be an acute angled triangle with ∠BAC=60∘\angle{BAC}=60^\circ and AB>ACAB > AC. Let II be the incenter, and HH the orthocenter of the triangle ABCABC . Prove that 2∠AHI=3∠ABC2\angle{AHI}= 3\angle{ABC}.
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