Figure 5: Use an arc of circle c1 to approximate the diameter passing through points A and B. The circle c1 is tangent to the diameter at O and its center O1 lies on the perpendicular bisector of the diameter. Define I1 as one of the intersections of the diameter and the defining circle γ. Locate O1 by rotating I1 about O counterclockwise by 90 degrees and then dilating by a factor equal to the radius of c1. Find the intersections P1 and Q1 of c1 and γ and use them as the endpoints of the circular arc a1. Note that the circle c1 is shown with a radius of 2 in order to make the details of the construction easier to see. When the radius is set equal to 1000, the arc a1 appears as a straight line.
Begin the construction by creating γ using the Circle[ <Point>, <Radius Number> ] and two points inside γ using the PointIn[ <Region> ] command.