Τρίτη, 17 Οκτωβρίου 2017

2003 IMO Shortlist G5

Let $ABC$  be an isosceles triangle with $AC = BC$, whose incentre is $I$.  Let $P$  be a point on the circumcircle of the triangle $AIB$ lying inside the triangle $ABC$. The lines through $P$ parallel to $CA$ and $CB$ meet $AB$ at $D$ and $E$, respectively. The line through $P$ parallel to $AB$ meets $CA$ and $CB$ at $F$  and $G$, respectively.  Prove that the lines $DF$  and $EG$ intersect on the circumcircle of the triangle $ABC$.


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