Therefore, the straight line running from B to A crosses circle with center O at the

common tangent point.

But consider the

common tangent to two circles at S and again at T in Figure 1.

* curves [s.sub.i] (x) and [s.sub.i+1] (x) admit a

common tangent in point [P.sub.i+1] where i = 0, ..., n - 1;

Example 1 Two circles and their common tangent lines

We will use MuPAD to create a scene with two given circles and their common tangent lines.

Example 2 Two circles and their common tangent lines (revisited)

In CAS we had to mimic all steps that we perform while solving the common tangent lines problem by hand.

The first thing I see is the following problem: "Given circles of radii 2 and 5, with centers 10 units apart, find the length of a

common tangent." Included in the figure are helpful auxiliary lines.

(3) In the case of C(2, 2, 2): For any common tangent line of two of the quadrics [[Gamma].sub.j](s) which is tangential to these in points P and Q resp.

Let the common tangent line to [[Gamma].sub.1] and [[Gamma].sub.2] through the intersection point be defined by the linear equation L = 0.

The two separating

common tangents [T.sub.1], [T.sub.2] of K and L intersect in a point p, and in the line pencil of p they define two open intervals.

For circular obstacles, the vertices of the visibility graph are the points of tangency of the

common tangents between two circles.