Proving Even Cycle in Graph Theory with 3 x-y Paths

[fibi257]

Hello! This question seems simple but I think I'll need your help to prove it.

Prove that if there are vertices x and y in V(G) such that G contains three independent x-y paths then G contains an even cycle.

Thank you in advance.

 

[disregardthat]

Hint: The paths are either odd or even.