2013 USAMO Problems/Problem 6
Revision as of 18:44, 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.