Trim arc line with two lines and removing trimed segment

How do i trim out ( Remove ) part B, with lines A ?
leaving the remaining Arc’s at C

Hi Glugwort,

find the intersection points between curve A and arc C,
use the resulting curve t parameter and the shatter component to split the arc.

image

If the curves in the centre already form a closed region, you could also use this approach.

image

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Thanks to you all for your help.

I can advance onto my next stumbling block.