Overlapping lines, create new two lines

Dear Dynamo Specialists,

I would like to get the answer of the next question. I have two lines: number 1 (black line and yellow) and de line of number 2 (black line, is a door line). The lines are overlapping each other, 2 on 1.

How can I cut line 1 by the line of 2?
It will create two lines (by cutting line 1 by 2), you can see the result in number 3.

Could anyone help me?

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@rlandkroon ,

that would be a starting point from a geometrical view

Okay! Thanks, but:

I have a list Red line and a list with the Blue line, first we have to search where the lines are overlapping.
Then the list of the Blue lines cut the Red lines and create a new list of the black lines.

Could you help me?

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@rlandkroon ,

you can catch them with boundingbox…