Ahri in late game

Hello, my name is Ari.

Before commenting: Yes, i am noob and i L2P, so i write this discussion.

So, few friends recommended me to try Ahri as mider. After Fiddlestick, i feel that Ahri dont have that much inpact in LATE game. Her probably lowest range atack from all range mages + Ulty that makes her to ge almost in team fight battle, it makes her very easy to die.

She is like Puck from Dota 2, but not Puck.

My late game build: http://i.imgur.com/vldg0ki.png 30% CD (To spam E CC as much as real) Swords (After each spell auto with ~300 dmg is kinda helpful against supports and full damage build carries) And max AP.

Any advices how to play Ahri in late? Tactics?

Thank you for answers!