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Turkey TST 1991 - P1

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March 13, 2011
ratiogeometrygeometry proposed

Problem Statement

Let C′,B′,A′C',B',A' be points respectively on sides AB,AC,BCAB,AC,BC of △ABC\triangle ABC satisfying AB′B′C=BC′C′A=CA′A′B=k \tfrac{AB'}{B'C}= \tfrac{BC'}{C'A}=\tfrac{CA'}{A'B}=k. Prove that the ratio of the area of the triangle formed by the lines AA′,BB′,CC′AA',BB',CC' over the area of △ABC\triangle ABC is (k−1)2(k2+k+1)\tfrac{(k-1)^2}{(k^2+k+1)}.
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