The term chord as used by geometers has an entirely different meaning and etymology from the term chord as used by musicians. The geometry term comes from the Latin chorda for bowstring, while the musical term comes from the Middle English cord, itself a shortening of accord.
So the chords of music and the chords of geometry are unrelated in that sense. Sometimes musicians talk about the Circle of Fifths, but this isn't a circle in the geometric sense; it is a way of visually organizing the 12 tones of the chromatic scale. Even if you used circle division for (musical) chords on the Circle of Fifths, I am not sure that anything useful would arise. Geometric patterns found by constructing (geometric) chords on a (geometric) circle laid atop the Circle of Fifths may or may not correspond to musical patterns, and this is as good a means as any for generating ideas, but this doesn't mean that it is a deeply meaningful theoretical notion.
That said, there is a long tradition of applying mathematics, including geometry, to music. I happen to have a copy of Tymoczko's A Geometry of Music, mentioned by @Richard in the comments. I must confess to not having read it, but only having skimmed over it a bit. It does look interesting, and is on my list of books to read more carefully. Looking in it again I see that Tymoczko develops a concept of pitch space, and a concept of a circular pitch-class space that is not organized in the same way as the Circle of Fifths. In a chapter entitled "A Geometry of Chords" he develops a concept of chord space that uses two-, three-, and higher-dimensional spaces. I don't see anything directly related to circle division or connecting geometric chords to musical chords here, though. You might also be interested in reading about negative harmony.