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.

The drawing in my earlier comment "Seriously", and much of my construction, would appear to hold in good stead for the construction required in this case.

I appear to have erred in considering that I should join the point X to the centre O.  In fact it would seem that I should locate Y lower by a somewhat different means and then join X to Y. 

By adjusting the pitch of line PE, and for that matter line PQ does not need to go through centre O, my drawings suggest that while the location of points X and Y will vary, the extended line XY is seemingly in exactly the same place.

These later thoughts have come from research which did not specifically identify this issue, but it was apparent. 

Since I am satisfied, I'll leave Bractals to either suggest any folly or else if I have given suffient hints.

Posted by brianjn on 2008-03-16 01:09:29