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Half of circle with diameter EF is tangent with BC,CA

Source: German MO 2009 481345

May 15, 2009
geometrycircumcircleprojective geometryperpendicular bisectorgeometry unsolved

Problem Statement

Let a triangle ABC ABC. E,F E,F in segment AB AB so that E E lie between AF AF and half of circle with diameter EF EF is tangent with BC,CA BC,CA at G,H G,H. HF HF cut GE GE at S S, HE HE cut FG FG at T T. Prove that C C is midpoint of ST ST.
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