Let be a convex quadrilateral such that and are not parallel and . The midpoints of the diagonals and are and , respectively. The line meets segments and at and , respectively. Show that .
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Let $ABCD$ be a convex quadrilateral such that $AB$ and $CD$ are not parallel and $AB=CD$. The midpoints of the diagonals $AC$ and $BD$ are $E$ and $F$, respectively. The line $EF$ meets segments $AB$ and $CD$ at $G$ and $H$, respectively. Show that $\angle AGH = \angle DHG$.
Izvor: Srednjoeuropska matematička olimpijada 2009, pojedinačno natjecanje, problem 3
Školjka 
be a convex quadrilateral such that 
and 
are not parallel and 
. The midpoints of the diagonals 
and 
are 
and 
, respectively. The line 
meets segments 
and 
, respectively. Show that 
.