# How to Find the centre of a circle, using two points on the circumference.

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.

• The picture suggests that the circle is tangent to the $x$ axis. That means you do have enough information to find its center. Is that enough help for you? – Ethan Bolker Apr 23 '17 at 13:05
• – Ethan Bolker Apr 23 '17 at 17:28

$CA = CB$, 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 $y_C$.