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Four points are concyclic in a square

Source: Czech and Slovak third round,2004,p5

March 3, 2012
geometrycircumcirclegeometry proposed

Problem Statement

Let LL be an arbitrary point on the minor arc CDCD of the circumcircle of square ABCDABCD. Let K,M,NK,M,N be the intersection points of AL,CDAL,CD; CL,ADCL,AD; and MK,BCMK,BC respectively. Prove that B,M,L,NB,M,L,N are concyclic.
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