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
Plugin 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.
Copyright 2006 by Alan
Cooper  page last modified on 7 May2006