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Inscribe circles in triangles using geometric construction, with PC geometry software such as Dr Geo on Linux. This slide show presents some innovative constructions. The slide show and included instructions are public domain. Basic use of compass and straightedge is advised as a prerequisite topic.
Clipping is a handy way to collect important slides you want to go back to later.
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http://www.slideshare.net/cmcallister/inscribe-semicircle-in-square-by-geometric-construction