Problem

Source: 11th CHKMO 2009

Tags: geometry, trigonometry, ratio, incenter, inradius, circumcircle, parallelogram



ΔABC is a triangle such that ABAC. The incircle of ΔABC touches BC,CA,AB at D,E,F respectively. H is a point on the segment EF such that DHEF. Suppose AHBC, prove that H is the orthocentre of ΔABC. Remark: the original question has missed the condition ABAC