Let gamma be a circle with center O and P a point outside gamma.
Construct a tangent line to gamma through point P using a straightedge only.
Prove the construction.
(In reply to Seriously
It is indeed true that "as / DPB widens, D, E and X approach each other, seemingly at point Y which is the apparent tangent intersection," but during that movement, Y also changes position. Y only approaches the tangent point as D and E also approach it. So in the general, secant, case, Y is not the point of tangency.
(I tried this out on Geometers Sketchpad; Y does move.)
Posted by Charlie
on 2008-03-15 10:11:24