A piece of broken plate was dug up in an archeological site. It was put on top of the grid where the

Notice that point X and Y both have the same x-coordinate. Let's assume we're dealing with a circle here.

Therefore, they exist on opposite sides of the circle. In fact, connecting point X and Y creates a line-segment that is also the diameter of the circle, shown below for reference.



By finding the distance from X to Y, then dividing by 2, we will have found the diameter, and subsequently the radius.

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]
\[X = (1,1); Y = (1,7)\]
\[d=\sqrt{(1-1)^2+(7-1)^2}\]
\[d=\sqrt{36}\]
\[d=6\]

Diameter is 6, therefore the radius is 3. Since X and Y are along the same plane, add 3 to 1 (1 being the y-coordinate of X). Therefore, the radius is at (1,4).

The equation for the circle, therefore is:

\[x^2+y^2=r^2\]
\[(x-1)^2+(x-4)^2=3^2\]

To test the third point Z, simply apply its coordinates into X and Y to check if it equals 9. It should...

Good luck