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angles wanted, in perimeter and areas bisectors passing through orthocenter

Source: Balkan MO Shortlist 2008 G3 BMO

April 6, 2020
geometryperimeteranglesarea of a trianglebisectororthocenterIMO Shortlist

Problem Statement

We draw two lines (ℓ1),(ℓ2)(\ell_1) , (\ell_2) through the orthocenter HH of the triangle ABCABC such that each one is dividing the triangle into two figures of equal area and equal perimeters. Find the angles of the triangle.
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