Fitting a plane to the flatter part of the tube

Hi,
I have a mesh of a tubular shape with cross-sections like these.

The cross-sections are flattened on one side.

There is also a centerline curve for the tube.
I would like to set up a local construction plane approximating the flat surface of the tube for a certain stretch of the tube.

The way I was thinking of doing this is by

1. making cross-sections between the given points on the centerline

2. looping through all possible chords to maximize the length of the chord and minimize the area it cuts off

3. fit a plane to points of all the chords selected in (2) for all cross-sections.

Am I on the right track, or is there a simpler way to do this?

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