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points on sides of a triangle, intersections, extensions, ratio of areas wanted

Source: Mexican Mathematical Olympiad 1997 OMM P5

July 28, 2018
ratiogeometryareas

Problem Statement

Let P,Q,RP,Q,R be points on the sides BC,CA,ABBC,CA,AB respectively of a triangle ABCABC. Suppose that BQBQ and CRCR meet at A′,APA', AP and CRCR meet at B′B', and APAP and BQBQ meet at C′C', such that AB′=B′C′,BC′=C′A′AB' = B'C', BC' =C'A', and CA′=A′B′CA'= A'B'. Compute the ratio of the area of △PQR\triangle PQR to the area of △ABC\triangle ABC.
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