2013 USAMO Problems/Problem 6
Revision as of 19:44, 11 May 2013 by Yuler1818181818 (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.