Final answer:
The question involves proving a geometric concept known as Monge's theorem which states that for three given circles, the intersection points of the external tangents are collinear.
Step-by-step explanation:
The question relates to the geometric properties of common external tangents to circles, where it is claimed that the three pairs of common external tangents to three different circles, when taken two at a time, will intersect so that the intersection points are collinear points. This is a classic result in plane geometry known as Monge's theorem. Monge's theorem states that for any three given circles in a plane (none of which is within another), the intersection points of the three pairs of lines, each line being the external tangents to two of the three circles, are collinear. This can be shown by considering pairs of circles and drawing the external tangents for each pair, then observing the points where these lines intersect.