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Consider /\ABC. Let I bet he incentre an...

Consider `/_\ABC`. Let I bet he incentre and a,b,c be the sides of the triangle opposite to angles A,B,C respectively. Let O be any point in the plane of `/_\ABC` within the triangle. AO,BO and CO meet the sides BC, CA and AB in D,E and F respectively. If `3vec(BD)=2vec(DC)` and `4vec(CE)=vec(EA)` then the ratio in which divides `vec(AB)` is` (A) `3:4` (B) `3:2` (C) `4:1` (D) `6:1`

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