2013 USAMO Problems/Problem 6
Revision as of 17:59, 3 July 2013 by Tenniskidperson3 (talk | contribs)
Let 
be a triangle. Find all points 
on segment 
satisfying the following property: If 
and 
are the intersections of line 
with the common external tangent lines of the circumcircles of triangles 
and 
, then ![\[\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1\]](http://latex.artofproblemsolving.com/1/a/0/1a00943b69bacf415bc36dc6a6b34ee278ddf0f6.png)
.
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
