IMO Shortlist 2009 problem G3
Dodao/la:
arhiva2. travnja 2012. Let
be a triangle. The incircle of
touches the sides
and
at the points
and
, respectively. Let
be the point where the lines
and
meet, and let
and
be points such that the two quadrilaterals
and
are parallelogram.
Prove that
.
Proposed by Hossein Karke Abadi, Iran
%V0
Let $ABC$ be a triangle. The incircle of $ABC$ touches the sides $AB$ and $AC$ at the points $Z$ and $Y$, respectively. Let $G$ be the point where the lines $BY$ and $CZ$ meet, and let $R$ and $S$ be points such that the two quadrilaterals $BCYR$ and $BCSZ$ are parallelogram.
Prove that $GR=GS$.
Proposed by Hossein Karke Abadi, Iran
Izvor: Međunarodna matematička olimpijada, shortlist 2009
Školjka 
