Exterior Tangents to Three Circles

Two nonintersecting circles have one pair of common interior tangents and one pair of common exterior tangents. The interior tangents intersect at a point on the segment between the the centers; the exterior tangents intersect outside that segment when the circles have different radii (otherwise they are parallel to the line joining the centers).
For three circles, there are three pairs of exterior tangents, one for each pair of circles. The intersections of those three pairs of exterior tangents lie on a line.
(You can drag the three circles.)


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D. Wells, The Penguin Book of Curious and Interesting Puzzles, New York: Penguin, 1993 p. 150.
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