Geometrical probability (part 2)

It doesn't matter where we place the first point on the circle (we can always rotate the figure without changing the probability). However, the next point can't be placed within 1cm of the first point, whether to the right or to the left. So we end up cutting out a 2cm arc from the circle's circumference, leaving us with $(2\pi-2)$ cm out of the whole $2\pi$ cm. They're randomly selected, so we can just divide the section where the event happens ( $\widehat{AB}>1cm$ ) by the whole sample space (the circle's circumference). This gives us $\frac{2\pi-2}{2\pi}=1-\frac{1}{\pi}\approx0.68169$