MathDB

2019.10

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

orthocenter wanted, projections of point on altitude on sides

Source: 2019 XXII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p10

5/4/2021
At the altitude AH1AH_1 of an acute non-isosceles triangle ABCABC chose a point XX , from which draw the perpendiculars XNXN and XMXM on the sides ABAB and ACAC respectively. It turned out that H1AH_1A is the angle bisector MH1NMH_1N. Prove that XX is the point of intersection of the altitudes of the triangle ABCABC.
geometryorthocenteraltitudeUkrainian TYM