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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 draw the dynamic diagram above for yourself.
Doing mathematics often involves observing and explaining properties of `invariance', that is, what remains the same when the rest of the pattern changes according to certain rules that can be described in mathematical terms. NRICH dynamic mathematics problems allow you to alter the diagrams and change some properties, so that you can observe what remains invariant. This may lead you to a conjecture that you can prove. Proving the result in the case of The Eyeball Theorem uses only similar triangles.