III.12 Proposition III.12
If two circles touch one another externally, the straight line joining their centres will pass through the point of contact.
Proof
Analogous to III.11. For externally tangent circles, the point of
contact A lies on the segment FG between the centres, and
FA+AG=FG exactly. The triangle inequality I.20 then forces
A to lie on the line FG.
lines 74–74 in main.tex
