Math

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

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*f²*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*.