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.
Circle γ has its centre O on the line PQ. Its circumference intersects PQ at B and C (B is nearer to P).
A line is drawn from P through γ such that D and E form a chord with D being nearer to p.
Draw a line from B through D until a line drawn from C through E intersect. From this point X construct a line to the centre O. The intersection of OX with γ is point Y.
Line PY forms the tangent to the given circle.
P B O C Q
I ask my reader to reconstruct the "imaginary" picture portrayed above.
The closest to a proof that I can give is:
DPB widens, D, E and X approach each other, seemingly at point Y which is the apparent tangent intersection.
Edited on March 15, 2008, 8:01 am
Posted by brianjn
on 2008-03-15 07:57:18