Geometry Problem 868: Cyclic Quadrilateral, Circle, Five Rectangles, Four Centers, Congruence. Level: High School, College, Mathematics Education

The figure below shows a cyclic quadrilateral ABCD. ABEF, BCGH, CDJK, and ADLM are rectangles of centers O₁, O₂, O₃, and O₄, respectively, so that AF = CD, BH = AD, CK = AB, and DL = BC. Prove that O₁O₂O₃O₄ is a rectangle.

 

See also:
Typography of problem 868.