Exterior Tangents to Three Circles
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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).[more]
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.)[less]
Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA
D. Wells, The Penguin Book of Curious and Interesting Puzzles, New York: Penguin, 1993 p. 150.
"Exterior Tangents to Three Circles"
Wolfram Demonstrations Project
Published: September 28 2012