# The longest straight line (L) within a polygon and the longest perpendicular line (T) to L

I'm mapping elongated glaciological features within QGIS 2.18.22 and I need to measure the longest straight line (L) and the longest perpendicular line (T) to L (as illustrated in the picture) within a mapped polygon (shapefile).

I have found the longest line by using the Oriented Minimum Bounding Box Tool, but this does not show me the location of T/the max width of the polygon, and I need to find this to determine the point B (see picture). ]1

1) From polygon create a points,

2) Then run the tool "Vector-processing geometry-Polygons Voronoi"

3) Select 2 extreme points along the length of the figure they will touch it, and 2 points across the width of the figure they will be closer than others from source polygon borders and run them tool "Vector-processing geometry-triangulation Delaunay"

see figure 2. This solution for QGIS.

4) And the best pick 4 and at 3 points 1) the first 3 points (extreme left, bottom middle and right extreme - triangulate - triangle will give you (L)) and 2) the second 3 points (top, left extreme, middle bottom - triangulate - triangle will give you (T)), then you can cross over them and in result to obtain figure "cross" see figure 3, got it, remove the excess edges.

P.S. don't forget blow up the triangles to extract the required lines : -)...