MathDB
2011 JBMO Shortlist G3

Source: 2011 JBMO Shortlist G3

October 8, 2017
geometryJBMO

Problem Statement

Let ABCABC be a triangle in which (BL{BL}is the angle bisector of ABC{\angle{ABC}} (LAC)\left( L\in AC \right), AH{AH} is an altitude ofABC\vartriangle ABC (HBC)\left( H\in BC \right) and M{M}is the midpoint of the side AB{AB}. It is known that the midpoints of the segments BL{BL} and MH{MH} coincides. Determine the internal angles of triangle ABC\vartriangle ABC.