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.
Školjka