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.

by solving the equation, y=5. The center is on the point (0,5) so the radius of the circle is 5.

We now have both the x and y values for the center of the equation as well as the radius so the equation of the circle is

 

Return to problem solving