MathDB

5

Part of 1997 Mexico National Olympiad

Problems(1)

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

Source: Mexican Mathematical Olympiad 1997 OMM P5

7/28/2018
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.
ratiogeometryareas