Dynamic Geometry 1477: Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

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Dynamic Geometry: Miquel's Pentagram Theorem. HTML5 Animation for Mobile Devices

HTML5 Animation for iPad and Mobile Devices
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Miquel Pentagram, Dynamic Geometry

Requires Java 1.3 or higher and Java enable browser
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).



Continue exploring at:
gogeometry.com/javacar/Miquel_1.htm

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.


Continue reading at:
gogeometry.com/miquel_pentagram1.htm