one of XB_1, OA_1 and C_1Y is equal to sum of other two
Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p1
April 18, 2022
geometryequal segments
Problem Statement
In a circle with center , chords and are drawn, both equal to the radius. Points , and are projections of points and , respectively, onto an arbitrary diameter . Prove that one of the segments , and is equal to the sum of the other two.(A. Shklover)