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This Demonstration gives a proof of Pompeïu's theorem: If ... is a point in the plane of the equilateral triangle ... , then there exists a triangle with side lengths ... , ... , and ... unless ... lies on the circumcircle of the triangle ... , when the triangle is degenerate. We rotate the equilateral triangle ... around the point ... by an angle of ... . This gives the triangle ... . As ... and ... , ... is equilateral, so ... . Also, ... and ... , so we have constructed ... whose sides have the same lengths as ... , ... , and ... .

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      EUN,LOM,LRE4,work-cmr-id:398185,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/PompeiusTheorem/,ilox,learning resource exchange,LRE metadata application profile,LRE

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