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Java-based: ran it and it -looks- sketchpaddy. Was able to make your construction in about six seconds.
http://www.geogebra.org/cms/index.php?option=com_frontpage&Itemid=1

More hardcore alternative, *nix and OSX only.
http://www.mit.edu/~ibaran/kseg.html

Both showed up for "open source Geometer's Sketchpad" alternatives.

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