  A triple chord is a sub-diagram of a chord diagram that consists of a circle
and finitely many chords connecting the preimages for every double point on a
spherical curve, and it has exactly three chords giving the triple
intersection. This paper describes some relationships between the number of
triple chords and an equivalence relation called strong (1, 2) homotopy, which
consists of the first and one kind of the second Reidemeister moves involving
inverse self-tangency if the curve is given any orientation. We show that a
prime knot projection is trivialized by strong (1, 2) homotopy, if it is a
simple closed curve or a prime knot projection without 1- and 2-gons whose
chord diagram does not contain any triple chords. We also discuss the relation
between Shimizu's reductivity and triple chords.
