Miquel Pentagram, Dynamic Geometry

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Take a pentagram ABCDE forming a convex pentagon FGHIJ and triangles AFJ, BGF, CHG, DIH, and EJI. Construct the circumcircles of triangles AFJ, BGF, CHG, DIH, and EJI. Then the five new points, K,L,M,N,P resulting from the intersection of two consecutive circumferences are concyclic (lie on the same circumference).



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Miquel s Pentagram Theorem

Interactive proof with animation and key theorems.
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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