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For EIGRP to determine a successor (best route), it uses the route with the lowest number of Feasible Distance(FD). And to determine the feasible successor (which is the backup route or the next best route) it uses the route with the lowest number of Advertising Distance(AD). My question is, why does it use AD(Advertising Distance) in choosing the next best route instead of FD(Feasible Distance) like it did for the best route?

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Because it doesn't guarantee a loop-free path. Comparing the reported distance against the feasibility distance does. Jeremy Stretch has a good write-up on it.

A route is entered into the EIGRP topology table as a feasible successor only if it meets the feasibility condition, which asserts that the reported distance of a route must be lower than the feasible distance of the current successor route.

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