Difference between revisions of "2013 USAMO Problems/Problem 6"
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| − | 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 | + | Let <math>ABC</math> be a triangle. Find all points <math>P</math> on segment <math>BC</math> satisfying the following property: If <math>X</math> and <math>Y</math> are the intersections of line <math>PA</math> with the common external tangent lines of the circumcircles of triangles <math>PAB</math> and <math>PAC</math>, then \[\left(\frac{PA}{XY}\right)^2+\frac{PB\cdot PC}{AB\cdot AC}=1. |
Revision as of 19:44, 11 May 2013
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.
