A line in the plane of a triangle intersects the sides and respectively at points and such that . Find the locus of the center of the circumcircle of triangle
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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
Školjka 
intersects the sides 
and 
respectively at points 
and 
such that 
. Find the locus of the center of the circumcircle of triangle 