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 by brianjn)

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