Let $ABC$ be an acute-angled triangle in which $\angle BAC = 60^o$ and $AB> AC$. Let $H$ and $I$ denote the points of intersection of the altitudes and angle bisectors of this triangle, respectively. Find the ratio $\angle ABC: \angle AHI$.
Problem
Source: 2010 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11
Tags: geometry, angles, orthocenter, incenter, Ukraine Correspondence