<Tri-2025-2266>, hint

Let OA=OB=OC=r and BM=tr.

Since BM=AM'=tr, BK/Ak=1 /t. Since triangles OLC and MLB are similar

BM/BO=BM/CO=tr/r=t=BL/CL. Similarly AK/BK=MA/BO=t.

Hence triangles OKB and OLC are congruent  ,thus <OKB=<OLC

Hence O,K,B,L are concyclic.