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Draw out a circle, and from the center of the circle draw a line, label this line 6 inches. Draw another line perpendicular to that line, that goes from one point of the circle to other side so that the 6 inch line cuts it in half. 
It should make a T shape, with the line coming out from the center is shorter than the chord. 

Because the 6 inch line reaches the chord at the midpoint, we can say that the 16inch line is cut into two equal sections of 8. If you draw a line connecting the center of the circle to one end of the chord, it forms a right triangle with one leg as 6 inches and the other leg as 8. Using these measurements, we can solve for the hypotenuse, which is also a radius of the circle. 

a² + b² = c²
6² + 8² = r²
36 + 64 = r²
100 = r²
r = 10

The radius of the circle is 10 inches.