Calculating line length within mulitple overlapping polygons using ArcGIS Desktop?

Question

My question is similar to Calculating edge length of polygon within overlapping polygon using ArcGIS Desktop?

However, my issue differs in that I have multiple overlapping polygons (upwards of 7) that share the same line.

Here's an example:

Polygons represent 50 meter buffers around a point and the line represents the edge of another polygon that I've clipped.

I'm trying to calculate the length of the blue line contained within multiple (yellow) polygons. The issue I'm running into is that I'm not able to calculate the length of the line within each individual polygon. I've tried Spatial Join and Intersect which haven't worked. Spatial Join results in the total length of the line regardless of polygon. Intersect segments the line by polygon border, therefore cutting off portions that should be included within a given polygon, i.e. length isn't calculated for a polygon that is overlapped.

I am using ArcGIS Desktop 10.6.

Answer 1

You can use arcpy and the da.UpdateCursor to iterate over each polygon and intersect with a dissolved line feature class, calculate length and write to a new field in the polygon feature class. Look at the documentation for Polygon and Polyline objects to understand disjoint, intersect etc.

import arcpy
polyfc = r'points_Buffer300m' #Name of polygon layer
linefc = r'line' #Name of line layer
linelength_field = 'linelen' #Name of field to hold lengths. Will be added below

arcpy.AddField_management(in_table=polyfc, field_name=linelength_field, field_type='DOUBLE')
arcpy.Dissolve_management(in_features=linefc, out_feature_class=r'in_memory\diss')
linegeometry = [i[0] for i in arcpy.da.SearchCursor(r'in_memory\diss','SHAPE@')][0]

with arcpy.da.UpdateCursor(polyfc,['SHAPE@',linelength_field]) as cursor: #Iterate over each polygon
    for row in cursor:
        if not linegeometry.disjoint(row[0]): #Check if polygon intersects polyline
            row[1]=linegeometry.intersect(row[0],2).length #Intersect the dissolved line geometry with polygon and calculate length of output line
        else:
            row[1] = 0
        cursor.updateRow(row)

Answer 2

In the picture below length of each line equal 100 m and radius of each circle is 75 m:

I intersected lines and circles and dissolve result using polygon id (NAME) as case field. As expected total length of lines equals to 150 m within each polygon: