+0 So I'm not sure if the book has the definitions wrong, but aren't external tangents not supposed to intersect the radi? I understand PQ is 20 and and how to calculate say the external tangent (19.6)
But If I were to imagine an "internal" tangent between both circules, wouldn't that just be the radi distances themselves? Maybe someone can shine some light into this for me? Not necesarily an answer but a point in the right direction? Thanks!!
+1632 Hi LioLaeus504!
By definition, a TANGENT is a line touching circles at one point that doesn't intersect through the circle (which would result in 2 points). That being said, a common external tangent cannot be through the circles, and thus cannot be the connections of the two centers...
And for your question, what it is asking is that imagine that PQ is extended infinitely to the right, and the external tangent (on top of the two circles) at some point intersects this line PQ at a point R. Continue from there and best of luck! 
