Intro: It is amazing that by a simple construction of 4 points on a line, elegant ratios of the of the GM can be obtained.

Problem: If P is a point on the chord AB (extended) of a circle such that the tangent at P which touches the circle at T is equal to AB. Draw C on AB such that PT =PC.

Prove: 1) AP/AB = phi

2) CA/CB =Phi

3 ) AP/AC = Phi^2

4) AP/BC = phi^3

5) How will you peform the construction in question ? For the problem take it that the construction is done.

Mally