Let \( C \) be a circle having centre in the first quadrant and touching the \( x \)-axis at a distance of \( 3 \) units from the origin. If the circle \( C \) has an intercept of length \( 6\sqrt{3} \) on \( y \)-axis, then the length of the chord of the circle \( C \) on the line \( x - y = 3 \) is:
