Problem

Source: Mumbai Region RMO 2014 Problem 3

Tags: trigonometry, geometry, angle bisector



Let ABC be an acute-angled triangle in which ABC is the largest angle. Let O be its circumcentre. The perpendicular bisectors of BC and AB meet AC at X and Y respectively. The internal angle bisectors of AXB and BYC meet AB and BC at D and E respectively. Prove that BO is perpendicular to AC if DE is parallel to AC.