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Archimedes' Twin Circles

Archimedes' Twin Circles Pick any three points on a line and use each pair of them to define a semicircle, as shown. Now draw a perpendicular between the two smaller semicircles. The two red circles will always have the same area. credit: Greg Ross http://www.futilitycloset.com/2014/03/20/archimedes-twin-circles/ Image: Wikimedia Commons also see: John Golden's work at http://mathhombre.blogspot.com/2014/03/archimedes-twin-circles.html