Using three drawings of a circle, students can develop the equation of a circle. Students first find 4 easy points that are 5 units from the center of a circle. Next the students use the Pythagorean Theorem to find that eight other points are also 5 units from the center. Then the students use another circle to show that for any point (x,y) on the circle the Pythagorean Theorem leads to an equation for a circle. .
Finally students discover that, in general, there is a general form for the equation of a circle.