G3

Part of 2008 Balkan MO Shortlist

Problems(1)

angles wanted, in perimeter and areas bisectors passing through orthocenter

Source: Balkan MO Shortlist 2008 G3 BMO

We draw two lines

(\ell_1) , (\ell_2)

through the orthocenter

H

of the triangle

ABC

such that each one is dividing the triangle into two figures of equal area and equal perimeters. Find the angles of the triangle.

geometryperimeteranglesarea of a trianglebisectororthocenterIMO Shortlist