Chemists usually talk about bond strength in terms of homolytic bond dissociation (each atom involved in the bond gets one electron back each, regardless of how electronegative it is relative to the other one). So-called bond dissociation energies, or BDEs, are measured homolytically. So that's why the O-H bond of water is around 119 kcal/mol whereas most C-H BDEs are in the 100 kcal/mol or less range. It might surprise you that an O-H bond is stronger than any C-H bond because you know that one can relatively easily deprotonate water whereas deprotonating a non-acidic hydrogen on an alkane is much harder (think ethane to form ethylene). This is because we're talking about homolytic BDEs when we talk about bond strength.
With that in mind, do this thought experiment. You do a homolytic cleavage of bond a and bond c. Which one will more readily cleave? Look at the products. If you break bond a, you get a two highly unstable radicals. If you break bond c, you get one unstable radical and another radical that is relatively stable - remember that tertiary radicals are more stable than secondary radicals are more stable than primary radicals because of the alkyl donating effect. So bond c should more readily cleave. So based on this analysis alone, I would predict bond c to be weaker than bond a.
However, as the above poster pointed out, since this is an allylic case, you can have hyperconjugation effects. If it is indeed the case that c is stronger than a, then it looks like the hyperconjugation effect wins out - but I don't see a way you can come to that conclusion without actually going out and doing the experiment.
