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, [MATH](x-a)^2 + (y-b)^2 = r^2[/MATH], 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: [MATH]a = -1, \; b = -\tfrac{1}{2} \; \text{and} \; r = \sqrt{\tfrac{85}{4}}[/MATH]. You can see the exact context in the image. Can someone help me solve this system of equations?
< broken attachment removed >
< broken attachment removed >