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I'm trying to find the equation of a circle, which I can easily work out if I knew the centre of it. However, the only information I'm given are two points on the circle that form a chord and an image that shows a rough placement of the circle on the grid. Image of the Circle. I was given this question by my teacher, so if no one can help me, I will go back to her to see if there is a solution.

Thanks for any help, Alex.

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$CA = CB$, so $C$ lies on the perpendicular bisector of $[AB]$, which is given by $x = 2$, so $x_C = 2$. Now, clearly, $D(2,0)$ is a point on the circle. Hence, the center lies on the perpendicular bisector of $[BD]$, which you can find its equation. Substituting the coordinates of $C$ in that equation you get $y_C$.

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  • $\begingroup$ Thank you I just realised that as I posted this question and I came out with an answer of (x-2)^2 + (y- 16/3)^2 = 100/9 , for the equation of the circle, however, feel free to say if you got a different answer. Thanks for the help though. $\endgroup$ – AdonisAB Apr 23 '17 at 13:19

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