P15

Part of 2016 Sharygin Geometry Olympiad

Problems(1)

right angle between centroid, circumenter and Nagel iff <A=60

Source: Sharygin Geometry Olympiad 2016 First Round P15 grades 9-11

O, M, N

be the circumcenter, the centroid and the Nagel point of a triangle. Prove that angle

MON

is right if and only if one of the triangle’s angles is equal to

60^o

geometryNagel pointright anglecircumcircle