it intersects the segment joining the centers of two circles
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They are the common tangents to the circles.
If the circles have the same radius then an infinite number, and if they do not, then none.
A common tangent is a line which is tangent to two (or more) curves.
From the definition of tangent, it can ONLY have one point in common called the tangent point.
Common Tangents Some common tangents of two circles can be drawn.You can find that the number of them varies by the condition of the distance and radii of two circles.Using the applet of Common Tangents, try to explore this relation to the common tangents. Using the applet of Common Tangents In this applet you can explore the number of common tangents, dragging to change the radii or to move the circles.The button of@"Init"@is for replacing the figure in the initial state.If you click the button of@"Auto",@the circles are moving automatically, and then you can enjoy their performance.