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concyclic , AS _|_ p

Source: Czech and Slovak Olympiad 1989, National Round, Problem 1

September 13, 2024
geometryConcyclic

Problem Statement

Three different points A,B,CA, B, C lying on a circle with center SS and a line pp perpendicular to AS AS are given in the plane. Let's mark the intersections of the line pp with the lines ABAB, ACAC as DD and EE. Prove that the points B,C,D,EB, C, D, E lie on the same circle.
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