IMO 1992 LL USA81

Suppose that points X, Y, Z are located on sides BC, CA,

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IMO 1992 LL USA81

Origin: USA

Problem

Suppose that points X, Y, Z are located on sides BC, CA, and AB, respectively, of \triangleABC in such a way that \triangleXY Z is similar to \triangleABC. Prove that the orthocenter of \triangleXY Z is the circumcenter of \triangleABC.