It seems the labelling for D and F is inter changed. When you interchange the labels for D and F the second question makes complete sense.
If you interchange the labels for D and F, The relationship is equality.
Which means AF=AD; DB=BE; EC=FC
This is because ABC is a triangle whose sides are tangents to the incircle. It is a standard property of a triangle which can be proven by considering the quadrilaterals AFID, BDIE, and CEIF(I is the Incenter, also in the above figure interchange D and F before considering these polygons)
Mar 8th, 2015
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