Notice in the picture above you are given 3 points that lie on a unique circle. Find the equation of the circle.
If I find the midpoint of the segment AB, what does that tell me about the x-coordinate of the circle?
In order to find the y-coordinate, I can use the distance formula since all radii of a circle are congruent. Let O be the center with coordinates (0, y); segment OA and OC are equal.