gg ess

Take graph paper, plot the three points and make a triangle.

Draw a circle inside the triangle to maximize the area of the circle.
Draw a circle outside the triangle that touches all three corners.

how to draw the circles:
https://www.youtube.com/watch?v=S5tyyOZBs1Q inscribed
https://www.youtube.com/watch?v=E2q27M-xSkw circumscribed

Circumscribing a triangle.
Here is a method for constructing the circle that circumscribes a triangle.

Draw the triangle.
Draw the perpendicular bisector to each side of the triangle. Draw the lines long enough so that you see a point of intersection of all three lines.
Draw the circle with radius at the intersection point of the bisectors that passes through one of the vertices. You should see that this circle passes through all three vertices, and that it is the desired circle.

Inscribing a triangle.
Here is a method for constructing the circle that inscribes a triangle.

Draw the triangle.
Draw the angle bisector for each angle of the triangle. Draw the lines long enough so that you see a point of intersection of all three lines.
Draw a line perpendicular to any side that passes through the intersection point. Mark the point on the side through which this line passes.
Draw the circle with radius at the intersection point that passes through the point you obtained in the last step. This is the desired circle.