Bird(s) of pray ID

At my school there is a large creek that runs through it. I am not exactly sure of were it goes to but that's another question. This creek brings some interesting birds such as various ducks, swamp-hens and a group of superb fairy-wrens. I seem to be the only one who notices these magnificent birds, which makes me disappointed that others can't see these things and share my interest. It is a bit of a distraction really, I am not sure wether to listen to my maths teacher or the grey teal calling outside the window. Anyway, today while I was on the park doing sport I heard the noisy minors attacking something. I turned to look and to my surprise I saw a large bird of pray swooping down into the creek, and trust me, it was a bird of pray. I suspect that it was trying to catch a duck inside the creek. I only saw the underside of the bird, from memory, it had a pale creamy-brown chest with a fairly long square like tail with a slightly darker tip. I think it would be easier to identify by it's habits and what it did. I am not sure what it was exactly but it think it was a brown goshawk because it says that it swoops through trees, ambushing it's pray.
I also saw a similar bird a few days ago, it was flying other my house in circles and then took of into the east. I believe it was also a brown goshawk because the description says it soars high on sunny days. Another thought might be peregrine falcon, yes, I said peregrine. I have seen it a few times around this area. I took a picture of the bird on my phone but it is very poor quality, not worth showing.
Most people don't believe I have seen all these birds, it's hard to convince myself that I have. I think that it comes down to if you wan't to see it. I mean, this bird was at the same spot which I was at that same time. Is it always there? Will it be there again? What I guess I am trying to say is what happens if I am not there and the bird was, or if I was inside and the bird was out?
So that's my bird of pray odyssey...