C.a.R. > Applications > Similarity and Angles> Golden Ratio

Here, you can see how the Golden Ratio is constructed. You can operate the green keys like a cassette player.

The construction works, since QB=AP. The circle has radius QB/2. Using the chord tangent theorem one sees QA*QP=QB^2. Thus QP is split in the Golden Ratio. Therefore, QC splits QB in the Golden Ratio too.

Technical Information

This is a special form of an applet, using keys to walk through a construction. It is possible, to set break points to stop only at certain interesting construction steps.