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).

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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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Contributed by: Izidor Hafner (September 2012)
Open content licensed under CC BY-NC-SA


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



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