External tangents to three circles.

Topic:
Circle
External tangents
  • Take any three circles(*).
  • Draw external tangent lines to each pair, and find the point of intersection.
  • The three intersection points (one point for each pair) lie on a straight line.
(*) Well, almost any three circles. There are exceptions, e.g. one circle cannot lie inside another one. Take any three circles for which it is possible to draw external tangent lines to each pair.....
Click through the construction. Can you prove this theorem?