IMO 2019 Shortlist G2
Let ABC be an acute-angled triangle and let D, E, and F be the feet of altitudes from A, B, and C to sides BC, CA, and A...
Category: Geometry
Problem
Let ABC be an acute-angled triangle and let D, E, and F be the feet of altitudes from A, B, and C to sides BC, CA, and AB, respectively. Denote by ωB and ωC the incircles of triangles BDF and CDE, and let these circles be tangent to segments DF and DE at M and N, respectively. Let line MN meet circles ωB and ωC again at P ‰ M and Q ‰ N, respectively. Prove that MP “ NQ. (Vietnam)