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.