A chord in a circle joins any two points on its circumference. Call these points A and B. We'll assume that AB is not a diameter, and we'll draw a diameter POQ parallel to chord AB. Where O is the centre of the circle, now we draw a radius OR perpendicular to the diameter and the chord, bisecting the chord at S. I'm not sure what you mean by section, but we'll assume that the section is defined by the length RS, that is, the part of the circle chopped off by the chord AB. RS would have length 2.9m given in your question. We'll assume that the 12m circle means its diameter, making its radius 6m, so PO=OQ=OR=AO=OB=6m=r, the radius. We'll also use the symbol s for the length RS=2.9m.
Now for some calculations. In the right-angled triangle ASO, AS is half the chord length. Let x=AS, so the chord length, c, is 2x. OS=r-s, the part of the radius chopped off by the chord. And AO=r. By Pythagoras, x^2+(r-s)^2=r^2. We can solve this to find x: x^2=r^2-(r-s)^2=s(2r-s); x=sqrt(s(2r-s)) so the chord length is 2sqrt(s(2r-s)). Put the values into this and we get: the chord length=2sqrt(2.9*9.1)=2sqrt(26.39)=2*5.137=10.27m approx.
To check the formula, chord length, c=2sqrt(s(2r-s)), put s=r and c=2sqrt(r^2)=2r, the diameter, so the chord is a diameter as we would expect. Put s=0, then x=0, because we haven't actually chopped off any part of the circle.
