Let be a convex quadrilateral with the line being tangent to the circle on diameter . Prove that the line is tangent to the circle on diameter if and only if the lines and are parallel.
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Let $ABCD$ be a convex quadrilateral with the line $CD$ being tangent to the circle on diameter $AB$. Prove that the line $AB$ is tangent to the circle on diameter $CD$ if and only if the lines $BC$ and $AD$ are parallel.
Izvor: Međunarodna matematička olimpijada, shortlist 1984
Školjka 
be a convex quadrilateral with the line 
being tangent to the circle on diameter 
. Prove that the line 
and 
are parallel.