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Lines AD, BE, and CF are concurrent

Source: IMO Shortlist 2000, G3

August 10, 2008
geometrycircumcircleorthocenterTriangleconcurrencyIMO Shortlistgeometry solved

Problem Statement

Let OO be the circumcenter and HH the orthocenter of an acute triangle ABCABC. Show that there exist points DD, EE, and FF on sides BCBC, CACA, and ABAB respectively such that OD+DH=OE+EH=OF+FH OD + DH = OE + EH = OF + FH and the lines ADAD, BEBE, and CFCF are concurrent.
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