Real IMO Shortlist 2019 G6 orthocenter wanted
Source: https://artofproblemsolving.com/community/c6h1896563p12956114
March 25, 2020
geometryorthocentercircleIncentersangle bisectorKvant
Problem Statement
A circle centred at is tangent to the sides , and of an acute-angled triangle at , and , respectively. Let and be the incenters of the quadrilaterals and , respectively. Let be an altitude of triangle . Let the internal angle bisectors of angles and meet the lines and at and , respectively. Prove that is the orthocenter of the triangle .Kolmogorov Cup 2018, Major League, Day 3, Problem 1; A. Zaslavsky