# Solving system equations with three unknowns

#### BasOomen

##### New member
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?

< broken attachment removed >

#### JeffM

##### Elite Member
I cant see the image. What are the points?

#### BasOomen

##### New member
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: $$\displaystyle B: \; a^2 + (4-b)^2 = r^ 2, C: \; (-4+a)^2 + (-4-b)^2 = r^2, P: \; (2-a)^2 + (3-b)^2 = r^2$$

#### BasOomen

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

#### Attachments

• 124.3 KB Views: 4

#### BasOomen

##### New member
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.