Mirror reflex triangles

Test your math skills with this LIMO 2021 exercise from Transtrend.

Mirror reflex triangles

Let ABC be a triangle. Somewhere within triangle ABC there is a smaller triangle A’B’C’ such that:

  • A’B’ is parallel to AB
  • B’C’ is parallel to BC
  • C’A’ is parallel to CA
  • A’ lies in between BC and B’C’
  • The surface area of A’B’C’ is times the surface area of ABC

➢ Determine the cumulative surface area of the triangles BCA’, CAB’ and ABC’ as a fraction of the surface area of ABC, expressed in terms of f.

Note: Your solution should hold for any triangle ABC, irrespective of the exact location of A’B’C’ within ABC.

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