IMO Shortlist 1984 problem 14
Dodao/la:
arhiva2. travnja 2012. Let
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
be a convex quadrilateral with the line
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
being tangent to the circle on diameter
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
. Prove that the line
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
is tangent to the circle on diameter
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
if and only if the lines
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
and
![AD](/media/m/6/9/6/69672822808d046d0e94ab2fa7f2dc80.png)
are parallel.
%V0
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