IMO 2008 Shortlist G1
In an acute-angled triangle ABC, point H is the orthocentre and A0, B0, C0 are the midpoints of the sides BC, CA, AB, re...
Category: Geometry
Problem
In an acute-angled triangle ABC, point H is the orthocentre and A0, B0, C0 are the midpoints of the sides BC, CA, AB, respectively. Consider three circles passing through H: ωa around A0, ωb around B0 and ωc around C0. The circle ωa intersects the line BC at A1 and A2; ωb intersects CA at B1 and B2; ωc intersects AB at C1 and C2. Show that the points A1, A2, B1, B2, C1, C2 lie on a circle.