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Answer:
Well, I think this is correct:
Well, if we know that a and b are parallel, that means they have the same slope but different y-intercept. So, if c and a intersects, then c and b are bound to intercept, because when c intersects with a, it will also cross b, since it will be going in the same route...which will make it also intersect with b. (crossing.)
Sorry if I'm wrong.
Hope this helps! :)