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ratio <ABC: <AHI, <BAC = 60^o, H orthocenter, I incenter

Source: 2010 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

April 26, 2021
geometryanglesorthocenterincenterUkraine Correspondence

Problem Statement

Let ABCABC be an acute-angled triangle in which ∠BAC=60o\angle BAC = 60^o and AB>ACAB> AC. Let HH and II denote the points of intersection of the altitudes and angle bisectors of this triangle, respectively. Find the ratio ∠ABC:∠AHI\angle ABC: \angle AHI.
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