Τρίτη, 17 Οκτωβρίου 2017

2004 IMO Shortlist G2

The circle $\Gamma$ and the line $l$ do not intersect. Let $AB$ be the diameter of \Gamma perpendicular to $l$, with $B$ closer to $l$ than $A$. An arbitrary point $C \ne A, B$ is chosen on $\Gamma$. The line $AC$ intersects $l$  at $D$. The line $DE$ is tangent to $\Gamma$ at $E$, with $B$ and $E$ on the same side of $AC$. Let $BE$ intersect $l$ at $F$ , and let $AF $ intersect $ \Gamma$ at $G \ne A$. Prove that the reflection of $G$ in $AB$ lies on the line $CF$ .

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