The equation of the chord of the circle S=0 with midpoint (x1,y1) is T=S1. Here T is obtained by the usual substitution at (x1,y1), and S1 is the value of S at (x1,y1). This is derived from the fact that the line from the centre to the midpoint is perpendicular to the chord. This formula is very efficient and avoids setting up perpendicularity conditions explicitly.