Stage: 4 Challenge Level: 
ABC is any triangle. D, E and F are arbitrary points on AC, AB and BC respectively. Circumcircles are drawn to the triangles ADE, CFD and BEF.
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
NOTES AND BACKGROUND
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.
epsilons. Dynamic geometry. Fibonacci sequence. Circle theorems. Generalising. Interactivities. Summation of series. Making and proving conjectures. Mathematical reasoning & proof. Angle properties of shapes.
Published February 1999,August 2008.
Copyright © 2007. University of Cambridge. All rights reserved.
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email: nrich@damtp.cam.ac.uk