How could Voldemort have gotten close enough to cast the spell?

I don't know if the thing / person becoming the Horcrux actually has to be in the vicinity of the one casting the spell. Also, I am not sure of the timeline - did Myrtle die before or after Voldemort found out about the Horcruces?

Harry as Horcrux? Intriguing; yes, that is certainly also a possibility, and an even worse one - in order to defeat Voldemort, Harry has to die?