Draw any three circles of different radii in a plane such that no circle is inside another - each must have interior points not in the interior or on the circumference of either of the other circles, to rule out the inside-but-tangent case. It is easiest to visualize this with non-overlapping circles, but overlapping will not "break" the result.
For each of the three pairs, draw the two common external tangents. For each two tangents, mark the point at which they intersect.
Prove that these three points are colinear.