I was reviewing an exam correction model and I stumbled upon a question about determining the equation of a circle. There were three points, all on the circle, which you could fill in into the standard equation for a circle, \(\displaystyle (x-a)^2 + (y-b)^2 = r^2\), in order to obtain a system of equations. They say you can solve this system but whenever I've tried this I've not come up with the right values: \(\displaystyle a = -1, \; b = -\tfrac{1}{2} \; \text{and} \; r = \sqrt{\tfrac{85}{4}}\). You can see the exact context in the image. Can someone help me solve this system of equations?
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