[url=http://artofproblemsolving.com/wiki/index.php?title=1974_AHSME_Problems/Problem_23]http://artofproblemsolving.com/wiki/index.php?title=1974_AHSME_Problems/Problem_23[/url] gives a problem which uses the external tangents theorem. [url=https://www.geogebra.org/m/napYF92Z ]https://www.geogebra.org/m/napYF92Z [/url]gives an illustration of the theorem and a bit of proof as to why it is true. The worksheet below gives additional practice problems using the theorem. You many want to draw in an additional line to make another right triangle that isn't seen immediately in the diagram.