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Construct Triangle Given 3 Points

Source: 1991 IrMO Paper 1 Problem 1

October 1, 2017
geometry

Problem Statement

Three points X,YX,Y and ZZ are given that are, respectively, the circumcenter of a triangle ABCABC, the mid-point of BCBC, and the foot of the altitude from BB on ACAC. Show how to reconstruct the triangle ABCABC.