## CommonTangent

Find a Line Tangent to Both of  Two Circles

[Run the Applet]
Note:  This applet uses a farily recent version of Java. As many browsers are not yet up to date, it is set up to use
Sun's Plug-in for Java (and will prompt you with how to install it if you don't already have it).

Note to Students and Teachers:
This applet explores the geometric construction of a line tangent to both of two given circles by a finite sequence of steps all of which can be done with just the basic Euclidean tools of ruler and compass.  It is of course quite easy in practice to just place the straight edge in almost the right position by trial and error. And the process of going back and forth to get tangency on each circle by rotating around the contact point on the other does converge exponentially fast. But the Euclidean ideal is to get an exact placement of the ruler by steps which involve just placing it across exactly located points rather than sliding it around while trying to watch both ends at once. There is in fact a fairly simple ruler and compass construction which gets the exact placement in a finite number of steps. The use of a java applet makes it easy to create diagrams for several steps of this process and to do so for a whole range of possible cases of the sizes and positions of the circles. This allows the user to quickly see that the claimed relationships are preserved and perhaps to gain some intuition as to why the construction works.

Note to Developers: The applet linked to above was built with the  GeX component library which is intended to support the quick construction of demonstration tools for mathematics instruction.

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