Tag Archives: Geometry

Miquel’s Pentagram Theorem

Take a convex pentagon FGHIJ, and prolong its sides until they intersects in points A, B, C, D and E, forming a pentagram. Construct the circumcircles of triangles AHG, DIH, BJI, EFJ and CGF. Then the five new points, F', G', H', I', J' resulting from the intersection of two consecutive circumferences are concycle, i.e., the points lie… Read More »