MathDB

3

Part of 2016 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

rioplatense perpendicularity

Source: Rioplatense Olympiad 2016 level 3 P3

9/4/2018
Let ABCA B C be an acute-angled triangle of circumcenter OO and orthocenter HH. Let MM be the midpoint of BC,NBC, N be the symmetric of HH with respect to A,PA, P be the midpoint of NMNM and XX be a point on the line A H such that MXMX is parallel to CHCH. Prove that BXBX and OPOP are perpendicular.
geometryperpendicularmidpointsCircumcenterorthocenter