Problem A. 581. (February 2013)
A. 581. In the plane, there are given two circles k_{1} and k_{2} with different radii, and a point O lying outside the circles. The endpoints of the tangents drawn from O to k_{1} are P and Q, the endpoints of the tangents drawn from O to k_{2} are R and S. The points P, Q, R, S are distinct. Let H be the external homothety center between k_{1} and k_{2}. Prove that if PR is not a external common tangent to the circles but passes through H then QS also passes through H.
(5 pont)
Deadline expired on 11 March 2013.
Statistics:
17 students sent a solution.  
5 points:  Bodnár Levente, Di Giovanni Márk, Fehér Zsombor, Herczeg József, Janzer Barnabás, Janzer Olivér, Kabos Eszter, Machó Bónis, Medek Ákos, Nagy Róbert, Omer Cerrahoglu, Sárosdi Zsombor, Szabó 789 Barnabás, Szabó 928 Attila, Williams Kada. 
4 points:  Maga Balázs, Zilahi Tamás. 
