Circle geometry help please

Hi guys, just need some help on some circle geometry.. Yucky C2 stuff >.<

Okay, so the question is as follows;
The points R(-4,3), S(7,4) and T(8,-7) lie on a circle.
(a) show that triangle RST has a right angle
(b) find the equation of the circle

I've had an attempt at part (a) and I thought the theory behind it was pretty straight forward - find the perpendicular bisector of two of the chords, find the centre of the circle from that and then find the distances between the vertices to prove that angle RST is in a semi circle, hence being a right angle. However, as I'm sure you can tell, that method is awfully long winded. Could someone please guide me in the right direction with this please.. Or perhaps I'm heading down the right path? Not too sure, any help would be greatly appreciated. Thanks guys!

For part a) show that two sides are perpendicular to eachother
Hint: m₁m₂=-1

O.. M.. G..
That was the first thing I did but then I went on to start proving that its a damn circle.. 15 of my precious time gone

Thank you very much for clarifying that. I feel so silly