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Fenerbahce started the game confidently and they could have been ahead after just 12 minutes when Bacary Sagna fired the ball against Raul Meireles but Wojciech Szczesny reacted well to prevent what would have been a fortunate goal.
Arsenal found the goal to relieve the pressure in the 25th minute as a mistimed tackle fell to Ramsey inside the box and the midfielder had the easy task of slotting the ball into the back of the net from close range.
Giroud was gifted a great opportunity to double his side's lead when Ramsey picked out the striker inside the box but the Frenchman's effort from a tight angle was blocked by Volkan Demirel.
Szczesny was called into action again shortly before the interval as Emmanuel Emenike forced the Polish goalkeeper to tip a powerful strike against the post.