Finding the area of a fraction of a circle defined by points on a grid. A grid is shown below, where the shortest distance between any two points is 1. Find the area of the circle that passes through points $X,$ $Y,$ and $Z.$



Can it be assumed that the arc created over each of the chord lengths shown will create a semicircle when put together? How can I determine what fraction of the circle passes through points X,Y, and Z to calculate the area?
Note that the distance $XY$ is $3$ units, where a unit is the length of the diagonal formed by the smallest square in the lattice, and $YZ$ is $4$ units. Does that strike anything?
As we know that a unique circle passes through three given points. Hence, if we assume the points $X, Y, Z$ as $(3, 3), (0, 0), (4, -4) $ the unique circle will be like this



Note: $X, Z$ are diametrically opposite points. Now, you can get answer.