find intersection of two contours/PathD partially overlapping

[andrei2popa]

When two contours/PathD have segments that partially overlap/touch, whether in a convex or concave manner, how can we identify the sub-paths, which may be multiple, within the overlapping region?
I tried to intersect them, returned nothing.
Thank you in advance! :)

[AngusJohnson]

If paths intersect then offsetting results will be undefined. I suggest you union these paths before offsetting.