The Mean Proportion

Move point Q and observe what happens.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

In the figure, PSR is a semi-circle and with PR as the diameter.  Given a rectangle with side QR, and a triangle PSR, a square is formed using its height. The  square has the same are as the rectangle.

Download GGB file here.