ABC is a triangle with the points D and E on the sides BC and AC respectively such that IBDI : IDC! = 4 : 1 and IAEI : IECI = 3 : 2. If AD and BE intersect at F, write down two equations using the facts that A, F and D are collinear and also B, F and E are collinear. Hence, or otherwise, find the ratios IAFI : IFDI and IBFI : IFEI
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