Problem

Source: 2015 Thailand October Camp FE & Geometry Exam p3

Tags: geometry, orthocenter, right angle, parallel



Let H be the orthocenter of acute-angled ABC, and X,Y points on the ray AB,AC. (B lies between X,A, and C lies between Y,A.) Lines HX,HY intersect BC at D,E respectively. Let the line through D parallel to AC intersect XY at Z. Prove that XHY=90o if and only if ZEAB.