Let ABCDE be a convex pentagon and extend the sides to form a pentagram A1B1C1D1E1. Construct the green circumcircles of the five yellow triangles. Then the five new points, A2, B2, C2, D2, E2 (blue points) resulting from the intersection of each pair of adjacent circles are concyclic (lie on the same circle). See dynamic diagram.
Auguste Miquel (France, Nantua, College des Castres.) published this beautiful theorem in Journal de Mathematiques Pures et Appliquees (Liouville ‘s Journal) Tome Troisieme, Paris 1838.
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Ten problems: 1411-1420
HTML5 and Dynamic Geometry
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