IMO 2016 Shortlist G5
Let D be the foot of perpendicular from A to the Euler line (the line passing through the circumcentre and the orthocent...
Category: Geometry
Problem
Let D be the foot of perpendicular from A to the Euler line (the line passing through the circumcentre and the orthocentre) of an acute scalene triangle ABC. A circle ω with centre S passes through A and D, and it intersects sides AB and AC at X and Y respectively. Let P be the foot of altitude from A to BC, and let M be the midpoint of BC. Prove that the circumcentre of triangle XSY is equidistant from P and M. 8 IMO 2016 Hong Kong