5 equal circles, intersections of 4 are vertices of a parallelogram
Source: Greece JBMO TST 2009 p2
April 29, 2019
geometrycirclesparallelogramequalcyclic quadrilateral
Problem Statement
Given convex quadrilateral inscribed in circle (with center and radius ). With centers the vertices of the quadrilateral and radii , we consider the circles . Circles and intersect at point , circles and intersect at point , circles and intersect at point and circles and intersect at point (points are the second common points of the circles given they all pass through point ). Prove that quadrilateral is a parallelogram.