Circuit(cyle)-hyperplanes in a graph

Question

Im currently working in matroid theory problem involving graphs. A circuit-hyperplane in a matroid is a circuit with |r| elements in a Flat of |r-1|. Translated into a graph the circuit-hyperplane will be a cycle or |r| edges on |n-1| vertecies. I've been playing around with their construction and have found that in a graph I cannot create two disjoint circuit-hyperplanes. My problem is I cant create/find a reason as to why. Can anyone point me in the right direction or a paper that will help.