how to join two ends to one?

Hi,
I'm making a swing for my kids in the backyard. Trouble is, I didn't buy
enough rope the first time, and so had to buy a second lot and figure out
how to join them. I need a knot to join two ends of one rope (going through
the tyre) to each end of the rope going around the tree. (I'm going to cut
the second rope in half and put each one through one side of the tyre, under
it and back up through, in a triangle shape, so that two ends of it come
back up to join the original rope) Can anyone help me?

thanks

geoff