Combine and Join Two Closed Paths With A Straight Path

Hi,
I have two closed path and I need to combine or join them with a straight path. When I selected all and right click to join, it did not join. Please refer to my screen shot. Thank you.

You can't create Y-junctions.
You can do one of two possbilities:
Just place the open path wherever you need and leave it there.
convert all of the shapes with Object > Path > outline stroke and then use the pathfinder functions.

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