Let be a cyclic quadrilateral whose diagonals and meet at . The extensions of the sides and beyond and meet at . Let be the point such that is a parallelogram, and let be the image of under reflection in . Prove that are concyclic.
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Let $ABCD$ be a cyclic quadrilateral whose diagonals $AC$ and $BD$ meet at $E$. The extensions of the sides $AD$ and $BC$ beyond $A$ and $B$ meet at $F$. Let $G$ be the point such that $ECGD$ is a parallelogram, and let $H$ be the image of $E$ under reflection in $AD$. Prove that $D,H,F,G$ are concyclic.
Izvor: Međunarodna matematička olimpijada, shortlist 2012
Ovaj zadatak me proganjao cijelu srednju školu. Imam G3 i G4, al nikako nisam mogao završit prokleti G2. I danas, nakon 4 godine je napokon pao. Najgore od svega je kaj sam ga dovršio TRIGONOMETRIJOM!! Mrzim trig i odvratno se osjećam, sad bi radije da ga nisam ni riješio.
Ovaj zadatak me proganjao cijelu srednju školu. Imam G3 i G4, al nikako nisam mogao završit prokleti G2. I danas, nakon 4 godine je napokon pao. Najgore od svega je kaj sam ga dovršio TRIGONOMETRIJOM!! Mrzim trig i odvratno se osjećam, sad bi radije da ga nisam ni riješio.
Školjka 
be a cyclic quadrilateral whose diagonals 
and 
meet at 
. The extensions of the sides 
and 
beyond 
and 
meet at 
. Let 
be the point such that 
is a parallelogram, and let 
be the image of 
are concyclic.