IMO Shortlist 1968 problem 14
Dodao/la:
arhiva2. travnja 2012. A line in the plane of a triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
intersects the sides
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
and
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
respectively at points
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
and
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
such that
![BX = CY](/media/m/7/4/a/74a19c67f3ff80fe9d2d9ca4f013c14c.png)
. Find the locus of the center of the circumcircle of triangle
%V0
A line in the plane of a triangle $ABC$ intersects the sides $AB$ and $AC$ respectively at points $X$ and $Y$ such that $BX = CY$ . Find the locus of the center of the circumcircle of triangle $XAY .$
Izvor: Međunarodna matematička olimpijada, shortlist 1968