Proposition

The figure below shows a cyclic quadrilateral ABCD. A circle O' meets AB, BC, CD, and AD at E, F, G, H, I, J, K, and L. EJ intersects to LG and KH at M and Q. FI intersects to LG and KH at N and P. Prove that MNPQ is a cyclic quadrilateral.
 

 

See solution below