The area of a segment and that of the circle are related by the angle at the centre; And the length of the arc and circumference are similarly related,
The two ratios are the same so we can write s/(2(pi)r)=a/((pi)r^2), where s=arc length, a=segment area, and r=radius.
This simplifies to s/2=a/r, from which r=2a/s=2*52/16=13/2=6.5cm.