To change triangle ABC and points D, E and F, click on the 'Move' icon (top left) and then click and drag any of the points.
Follow the instructions to draw the circumcircle BEF in the dynamic diagram below.
What do you notice about the three circumcircles?
Can you prove your conjecture?
Created with GeoGebra
This dynamic image is drawn using Geogebra, free software and very easy to use. You can download your own copy of Geogebra from http://www.geogebra.org/cms/ together with a good help manual and Quickstart for beginners. You may be surprised at how easy it is to drawdynamic diagrams for yourself.