MathDB

G4

Part of 2008 Balkan MO Shortlist

Problems(1)

barycenter of intersections of perp. bisectors of GA,GB,GC is the orthocenter

Source: Balkan MO Shortlist 2008 G4

4/6/2020
A triangle ABCABC is given with barycentre GG and circumcentre OO. The perpendicular bisectors of GA,GBGA, GB meet at C1C_1,of GB,GCGB,GC meet at A1A _1, and GC,GAGC,GA meet at B1B_1. Prove that OO is the barycenter of the triangle A1B1C1A_1B_1C_1.
Centroidorthocentergeometryperpendicular bisectorbarycenter