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O,K,C,L, concyclic wanted, <CLO = < BLM starting with isosceles ABC

Source: All-Russian MO 2002 Regional (R4) 9.3

September 17, 2024
geometryConcyclic

Problem Statement

In an isosceles triangle ABCABC (AB=BCAB = BC), point OO is the center of the circumcircle. Point MM lies on the segment BOBO, point M′M' is symmetric to MM wrt the midpoint of ABAB. Point K is the intersection point of of M′OM'O and ABAB. Point LL lies on side BC such that ∠CLO=∠BLM\angle CLO = \angle BLM. Prove that points O,K,B,LO, K,B,L lie on the same circle
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