How Stupid am I or how Brilliant is this Play?

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$5000 buyin NLHE tournament at the Commerce with 10,000 in chips to begin with.

I'm having a tough time having lost half my chips 20 minutes into the event. We're in level three with blinds of 50/100.
It's ninehanded but only six players are present and I open raise to 350 in the effective cutoff with QTo. BB calls.
I have around 4200 left and he has around 10000 left. BB lost T12000 around 20 minutes earlier playing a draw hard and then having his river bluff picked off.

Flop comes Q 3 8 rb

I bet 450 and he makes it 1100. I should have folded.

Turn Q 3 8 9. He pushes and I call.

Comments appreciated. Results to follow.

Bruce

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Call a check raise with top pair, medium kicker for what will likely be all of your chips by the river? A C/R of 1/4 your stack is sure to pot commit you before the river, assuming you call down. Unless you have an incredible read on this guy, get out before there's no turning back with your mediocre hand. There's still plenty of time to comeback from your early losses.

You said in an hour you hadn't picked up any of his patterns... which makes this a fold for sure. Had you paid more attention during that hour and picked up some useful info you might be able to take a different line.

I can see this as a possible play that BB knows will pot commit you, with the hope that you won't risk your tournament life by calling his push. Like I said, you'd need a great read to know if this was the case for sure.