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Part of 1978 IMO Shortlist

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Prove that SB'M and SA'N are similar - ISL 1978

Source:

9/20/2010
Two identically oriented equilateral triangles, ABCABC with center SS and A′B′CA'B'C, are given in the plane. We also have A′≠SA' \neq S and B′≠SB' \neq S. If MM is the midpoint of A′BA'B and NN the midpoint of AB′AB', prove that the triangles SB′MSB'M and SA′NSA'N are similar.
symmetrygeometrysimilar trianglesEquilateral TriangleIMO Shortlist