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orthocenter and circumcenter - IMO LongList 1992 USA4

Source:

September 2, 2010
geometrycircumcircleorthocenterCircumcenterIMO ShortlistIMO Longlist

Problem Statement

Suppose that points X,Y,ZX, Y,Z are located on sides BC,CABC, CA, and ABAB, respectively, of triangle ABCABC in such a way that triangle XYZXY Z is similar to triangle ABCABC. Prove that the orthocenter of triangle XYZXY Z is the circumcenter of triangle ABC.ABC.
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