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common chord of circumcircles perpendicular to a triangle side

Source: 2014 Sharygin Geometry Olympiad Final Round 9.5

August 3, 2018
geometrycirclesperpendicular

Problem Statement

In triangle ABCABC ∠B=60o,O\angle B = 60^o, O is the circumcenter, and LL is the foot of an angle bisector of angle BB. The circumcirle of triangle BOLBOL meets the circumcircle of ABCABC at point D≠BD \ne B. Prove that BD⊥ACBD \perp AC.
(D. Shvetsov)
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