IMO Shortlist 2000 problem G6
Dodao/la:
arhiva2. travnja 2012. Let
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
be a convex quadrilateral. The perpendicular bisectors of its sides
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
and
![CD](/media/m/8/9/5/895081147290365ccae028796608097d.png)
meet at
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
. Denote by
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
a point inside the quadrilateral
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
such that
![\measuredangle ADX = \measuredangle BCX < 90^{\circ}](/media/m/8/1/a/81a6f2b4d3b073428bb4ea7cd9190bc1.png)
and
![\measuredangle DAX = \measuredangle CBX < 90^{\circ}](/media/m/5/5/d/55d7714234d3de0447990f2612cd6401.png)
. Show that
![\measuredangle AYB = 2\cdot\measuredangle ADX](/media/m/c/4/a/c4a51ece476754f502fc3e9775f08a12.png)
.
%V0
Let $ABCD$ be a convex quadrilateral. The perpendicular bisectors of its sides $AB$ and $CD$ meet at $Y$. Denote by $X$ a point inside the quadrilateral $ABCD$ such that $\measuredangle ADX = \measuredangle BCX < 90^{\circ}$ and $\measuredangle DAX = \measuredangle CBX < 90^{\circ}$. Show that $\measuredangle AYB = 2\cdot\measuredangle ADX$.
Izvor: Međunarodna matematička olimpijada, shortlist 2000