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Cyclic Points form Right triangle

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December 9, 2010
algebrafunctiondomainvectorgeometrycircumcirclegeometry unsolved

Problem Statement

Five distinct points A,B,C,DA, B, C, D and EE lie in this order on a circle of radius rr and satisfy AC=BD=CE=rAC = BD = CE = r. Prove that the orthocentres of the triangles ACD,BCDACD, BCD and BCEBCE are the vertices of a right-angled triangle.
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