The Problem of Apollonius

Problem: The Problem of Apollonius

To construct a circle tangent to three given objects -- points, lines, or circles.

A point if "tangent to" a circle if it is on the circle.

The problem is posed for "general position" -- that is, objects arranged so that constructions are possible.

Discussion/Solutions? :

There are 10 classes of constructions for this problem.

1. 3 Points (PPP)

2. 2 Points and 1 Line (PPL)

3. 2 Points and 1 Circle (PPC)

4. 1 Point, 1 Line, and 1 Circle (PLC)

5. 1 Point and 2 Lines (PLL)

6. 1 Point and 2 Circles (PCC)

7. 1 Line and 2 Circles (LCC)

8. 2 Lines and 1 Circle (LLC)

9. 3 Lines (LLL)

10. 3 circles (CCC)

Return to Susie Lanier's Class Page.