Solving system equations with three unknowns

[BasOomen]

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?

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[JeffM]

I cant see the image. What are the points?

 

[BasOomen]

I cant see the image. What are the points?

The image has the correction model which shows the points, filled into the general equation for a circle: [MATH]B: \; a^2 + (4-b)^2 = r^ 2, C: \; (-4+a)^2 + (-4-b)^2 = r^2, P: \; (2-a)^2 + (3-b)^2 = r^2[/MATH]

 

[BasOomen]

Maybe you can see the full image now (I've changed it to a JPEG-format).

 

[BasOomen]

There was a mistake in my writing which resulted in me using the right method but not getting the right answer. I noticed this after someone solved it for me.