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A moves on major arc BC and some point is on the same distance from BC

Source: 2021 Oral Moscow Geometry Olympiad grades 10-11 p3

May 17, 2021
geometryangle bisectorcircumcircle

Problem Statement

Circle (O)(O) and its chord BCBC are given. Point AA moves on the major arc BCBC. ALAL is the angle bisector in a triangle ABCABC. Show that the disctance from the circumcenter of triangle AOLAOL to the line BCBC does not depend on the position of point AA.
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