A circle has two parallel tangents and. A circle touches at and at . A circle touches at , at and at . The lines and meet at . Show that is the circumcenter of
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A circle $C$ has two parallel tangents $L'$ and$L"$. A circle $C'$ touches $L'$ at $A$ and $C$ at $X$. A circle $C"$ touches $L"$ at $B$, $C$ at $Y$ and $C'$ at $Z$. The lines $AY$ and $BX$ meet at $Q$. Show that $Q$ is the circumcenter of $XYZ$
Izvor: Međunarodna matematička olimpijada, shortlist 1994
Školjka 
has two parallel tangents 
and
. A circle 
touches 
and 
. A circle 
touches 
, 
and 
. The lines 
and 
meet at 
. Show that 