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A Geometry Puzzle in a Regular Nonagon

Two chords are drawn on a regular nonagon from the midpoint of a side to vertices that are three and four vertices away and three edges apart. A line through the midpoints of these chords is parallel to a diagonal of the nonagon and close to it. What is the distance between that line and that diagonal? The regular nonagon has side length one.

Point M is the midpoint of edge AB of a regular nonagon. Two chords MD and MI are drawn from M to vertices D and I respectively. A line is drawn through the midpoint of these chords. It is parallel to the diagonal DI of the nonagon and close to it, but just a little further from the centre of the nonagon.

Introduction

Welcome to my blog about mathematics and technology, with a bit of philosophy. My interests include plane geometry, basic number theory, and computer software. My first posts will explore geometric constructions using computational geometry software. The Fibonacci sequence, algebra, trigonometry and some programming algorithms may be thrown in too.