MathDB

5

Part of 2009 German National Olympiad

Problems(1)

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

Source: German MO 2009 481345

5/15/2009
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.
geometrycircumcircleprojective geometryperpendicular bisectorgeometry unsolved