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Cyclic points [variations on a Fuhrmann generalization]

Source: China TST 2006

June 18, 2006
geometrycircumcirclegeometry unsolved

Problem Statement

HH is the orthocentre of △ABC\triangle{ABC}. DD, EE, FF are on the circumcircle of △ABC\triangle{ABC} such that AD∥BE∥CFAD \parallel BE \parallel CF. SS, TT, UU are the semetrical points of DD, EE, FF with respect to BCBC, CACA, ABAB. Show that S,T,U,HS, T, U, H lie on the same circle.
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